I often see gay/bisexual/trans rights, economic justice, and support for a "constitutional right" to abortion being lumped together. But I think there's a vast difference between the first two issues and the last one. I don't judge others who disagree with me about this; there are reasonable people on all sides of the abortion debate. But nevertheless, I just felt it'd be appropriate for me to share a few thoughts.
No matter whether one is pro-choice or pro-life, it's important for one to realize that constitutional decisions not be based merely on the personal predilections of the judges considering them (does anybody remember that obscure Bush v. Gore case?). A judge's job is not to adjudicate how much he or she agrees with the public policies being challenged. I should note that I'm far from a constitutional conservative -- or any other kind of conservative. For instance, I believe that bans on gay marriage violate the Equal Protection Clause of the 14th Amendment. I believe in full equality for trans persons. I'm economically liberal. I would strongly support a drastic increase in the size of Medicaid, food-stamps, and all other programs intended to help the most needy.
But nevertheless, the notion that the Constitution somehow protects a "right to abortion" is beyond absurd; it is not even minimally plausible. Because the states have an overwhelmingly-compelling interest in protecting [what they believe to be] unborn children from being killed, there is not the slightest bit of justification for striking abortion-laws down. Not even from the most liberal, "living constitution"-interpretation imaginable. Not even if there were a clause in the Constitution that explicitly provided an expansive right to privacy.
One does not need to be an "originalist" or "strict constructionist" to realize this. It seems clear that gay couples have a right to marriage equality based on the 14th Amendment, partly because there simply is no rational state-interest achieved by restricting marriage to opposite-sex couples; it is completely arbitrary and purely discriminatory to say that opposite-sex couples can marry but same-sex couples can't. Such a distinction is utterly meaningless, as absolutely no one gets harmed when gay couples marry. When it comes to legalized abortion, on the other hand, there certainly is a tremendous state-interest in protecting the unborn child from being killed (one may not agree that the unborn are persons, but indeed, it is never required that everyone personally agree with the laws in their states).