Moderates are important, they are the often the pragmatic ones who make the right choices even if it breaks ideology or comes at a cost. As Jon Stewart said, they're often not paid attention to by the media or politicians, because "moderates never take to the streets, shouting 'Be Reasonable!'"
Ignoring them, sidelining them, de-legitimizing them is how extremists of any sort get their way. When you ignore the moderates, you empower the hawks. The hawks give the opposing side justification to steamroll everyone to carry out your plans.
Let's explain this point with 3 examples from history, before we look at the current Israel-Palestine conflict on the news
In 2003, Iranian President Khatami made an offer to George W. Bush. Iran offered recognition of Israel within 1967 borders, to put pressure on Hizbullah and the Palestinians to moderate, signing the additional protocols of the nuclear Non-Proliferation Treaty to outlaw weapons development, and full cooperation with the International Atomic Energy Agency. What the Iranians wanted in return was an end to U.S. hostility and sanctions, and recognition of Iran as a legitimate power in the region. Everything Bush was demanding Iran do, it was all on the table.
What did Bush do?
He reprimanded the Swiss embassy, which takes care of US affairs in Iran, for daring to forward this proposal to the State Department.
Bush and his various supporters (the military-industrial complex, the Christian Right, the Zionist Lobby, and Big Oil) do not want peace with Iran.
President Mohammad Khatami was seen as a moderate who was cozy with Iranian liberals, and was trying to bring Iran back into the international community and reduce tensions. When his policies of negotiating with the US failed to show any success, voters forced him out. How delighted Bush and his constituents must have been when the buffoon Mahmoud Ahmadinejad replaced Khatami and the hardliners took control, after the Bush administration had done what it could to sabotage the Iranian reform movement.
Bush (and his backers) put Iran right where he wanted it, in the sights of an ICBM.
Pushing Iranian moderates away and gave Republicans ammo to claim that Iran was a world threat, that its president was a Holocaust-denier, and must be militarily attacked to protect Israel. Back in 2006 the Likud party's backers in America started a campaign to paint Iran as the Fourth Reich. AIPAC and the neocons and the Saudi king were all itching for war with Iran, and getting rid of the moderate voices helped sell their case that Iranians were evil.
This is merely an example of a how extremists of any sort get their way. When you ignore the moderates, you empower the hawks. The hawks give you justification to steamroll everyone to carry out your plans.
Martin Luther King was another example. You have a prominent African-American leader who is well-spoken and religious, and announces non-violent policies to bring about racial peace. Racists utterly despised him, and tried propagandizing against him in every way they could, because they saw him as a threat to their interests. They had been trying to paint civil rights workers as agitators, subversives, and racists of the Malcolm X 50's sort, and King broke that narrative for them. The fact that King was meeting with President Johnson and racking up a string of victories made them terrified, he had to be taken out. J. Edgar Hoover, the head of the FBI, created a classified COINTELPRO campaign to harass him, blackmail him, and pressure him to suicide. Eventually someone assassinated him, and the moderates in the Civil Rights campaign were dealt a strong blow. (Malcolm was also assassinated after making it clear he was no longer advocating racial conflict) What was the result? Hawks and hardliners all ascended to power in their absence; Stokely Carmichael, the Black Panther party, Lewis Farrakhan, the rise of the Black Power movement, etc. The Ku Klux Klan and Strom Thurmond had to have been secretly overjoyed by this, it gave them far more talking points and the ability to fearmonger their way to more support.
We see this today in the American and European Muslim communities too. There are millions of patriotic law-abiding Muslims who are struggling for their Civil Liberties; an end to discrimination, and free practice of their religion, while Islamophobes try to sow fear and mistrust and even hate crimes. How do islamophobes do this? Since they can't appeal to racism or bald religious bigotry (in public anyway), they do this portraying the Muslim community at large all as terrorists or terrorism-supporters. We have overwhelming evidence that terrorism and its ideologies are not mainstream, but they want people to forget this inconvenient fact. This is why islamophobes like Pamela Gellar and Robert Spencer devote a LOT of time trying to attack moderate Muslim leaders like CAIR or ICNA or ISNA. They spend more time writing long diatribes against scholars like Hamza Yusuf or Tariq Ramadan, picking apart and overanalyzing every sentence they make, than they do paying attention to actual extremists. Robert Spencer devotes far more time arguing against Tariq Ramadan's calls for patriotism than Bin Laden's actual speeches against Western ideas. Clearly Ramadan is a bigger threat to Spencer's goals than bin Laden was; 9/11 made Spencer rich.
This came to mind today, because Israel has put itself into a position where the moderates are not in power in Gaza, and are now stuck with no solutions. When Arafat was in power, Israel refused to deal with him, so Israelis elected Mahmoud Abbas, a moderate who promised he could work with Israel and Palestinians and negotiate a peace. Israel's right-wing government didn't like the idea of an actual compromise, so worked hard to marginalize him, first by badmouthing him and then funding his opponents. The Israeli government destroyed police stations and government buildings in airstrikes, which became one of the talking points in the 2005 Palestinian election; "why vote for Abbas when Israel clearly shows him no respect, his policy of talking to Israel is not working, let's vote for a group that can actually force Israel to stop rather than a politician who likes to appear in front of cameras." The result was people voted for Hamas. Just like Iranians, people in desperation turned to someone who promised action after words and dialogue failed.
There is no doubt that Israel's government under Likud leadership has been working very hard to give moderates the runaround, and steer all media focus on the hardline Palestinian opponents. First of all, Benjamin Netanyahu said he couldn’t talk to Abbas because he didn’t also represent Hamas. Then when Abbas formed a unity government, Netanyahu said he couldn’t talk to Abbas because he had unified himself with the “terrorist” Hamas. Now he says he can only talk to him if he breaks with Hamas – even though he won’t then represent Hamas. It's an odd irony since Israel cultivated religious groups in Palestine decades ago in order to foment opposition to Arafat and the secular PLO. With Palestinians dividing into factions, they were weakened for Israel's benefit. This isn't a conspiracy theory, Mossad admits that this was one of their mistakes in hindsight.
The Israeli government froze the scheduled tariffs and duties that were promised under the Oslo accords, making the PLO go too broke to pay its police force, meaning they couldn't suppress Hamas (and driving many more disgruntled workers to support Hamas) or prevent attacks on Israel. This article from a few days ago pointed out a few other examples of how Israel keeps refusing to help Abbas even when it's in Israel's best interests. Also, the Palestine Papers leak showed that Abbas offered to give away all of Jerusalem in exchange for any two state solution and Israel's government turned down the offer with no counter-offer. When this leak hit the media, public opinion of Palestinians turned sharply away against Abbas. People called him a useless sell-out for offering to give away their most precious assets (Jerusalem) and in exchange getting nothing in return.
What can we do? Stick with the goal of peace, no matter what. Obama resisted the neocons and war hawks and insisted on talks with Iran before any further sanctions. He strengthened moderate Iranians by reducing some sanctions as a reward for engaging in talks in the first place. The reason the White Power movement didn't take root in MLK's absence was because there were still moderates left to continue the fight; President Johnson barely passed the Civil Rights Act when King was alive, but used King's death as motivation to pass Voting Rights Act, despite charged rhetoric and threats from both directions.
In the case of Palestine, the proper course of action, according to many experts, would be for Israel to strengthen moderate Palestinian factions and use them as part of the effort to eradicate terrorism in Palestine, if that was Israel's actual goal. Abbas bet his career on the idea that security cooperation with Israel and public recognition of Israel’s right to exist are more likely to bring the Palestinians peace than Hamas' tactics of rockets, but it’s not working out so well for him. It’s hard for Abbas to convince Palestinians that forming a state through nonviolence is succeeding when Israeli settlements gobble up more and more of the land on which Palestinians might build their state. Abbas has frequently complained to the media about this, saying it's the equivalent of two people negotiating over how to split an ice cream, but one keeps eating it while they're discussing how much each person should get.
Abbas CAN be strengthened, but Netanyahu deliberately refuses to do so. Some say it's because as a right-winger, he does not see Abbas and Hamas as fundamentally different; the Israeli Foreign Ministry called Abbas' plan to join the UN "diplomatic terrorism." Others say that it's a Machiavellian tactic because keeping Palestinians divided and fighting one another means Israel can continue it's settlements and provide an excuse why he won't reach out for a deal with Palestinians. (Also, Israel has a long policy of killing or jailing anyone who could be the Palestinian Mandela)
"So how do you suggest Abbas be strengthened if you feel that the Palestinian people have lost faith in him?" is what some asked me in response. Simple; give him something. Here's one hypothetical news headline: "Abbas successfully negotiates the release of 10 year olds from Israeli prisons." Or "Abbas convinces Israel to allow limited number of Palestinians in West Bank to visit relatives in Gaza for the first time in a decade. " It isn't hard, the public originally elected him thinking he was a guy who could replace Arafat (whom Israel flat-out refused to talk to) and successfully get Israel to recognize their grievances and work for peace. When the Likud party and Israeli government decided to try the same runaround with Abbas as they did with his predecessors, the public gave up and concluded that Israelis only respect force.
Like I said, if Israel's government actually cared about pursuing peace, they'd cultivate him as an ally and offer carrots and sticks. They have shown Abbas zero carrots and hit him with many sticks, causing him to go back to his people in disgrace, and Hamas was strengthened. You have an Israeli government that absolutely does not care about hearts and minds, and shows they aren't legitimately looking for solutions. The Likud party in its greed wants all the land, and is not willing to settle for peace. (In this, they are Hamas' mirror image; they want to drive the Arabs into the sea or Egypt, they have no problem inflicting violence on civilians, either in Gaza or lynching farmers on the West Bank, and are just as maximalist in their demands and fascist in their rhetoric to the point where they praise Jewish terrorists like Yigal Amir and Baruch Goldstein and build shrines to them. The biggest difference in many Arab eyes is that they have better PR.)
The only way out of this conflict is to dump the right-wingers running Israel and actually sit down with Palestinian leaders to negotiate a Two-state solution. (I'd do the same with Palestine, if Israel hadn't assassinated the moderates recently.) Abbas has asked for an end to settlement construction, they should grant it as a show of good faith, then Abbas will reciprocate with enforcing a cease-fire, and Israel will restrain the settler violence AND actually hold up their own end of the ceasefire (Israel broke the last 2, in 2012 by assassinating a Hamas negotiator, and in 2008 by crossing the border and killing 6, and the unprovoked shelling of a beach in 2006, killing several Palestinian children and triggering reprisal attacks).
When you take away hope, people will turn to militant groups. Abbas' position today is weak because it shows how completely powerless he is; his goals and strategy for dealing may sound nice but the public no longer believes Israel will hear him nor will he be able to get anything done. Change that and you'll see actual movement to peace.