The Supreme Court is not joining various Republican-controlled states in their rush to allow anti-gay business owners to turn gay customers away. The Court will not hear
Elane Photography v. Willock, an appeal brought by a photographer who refused to photograph a lesbian wedding. But it's
not clear that this is the final word on this issue:
At one point, the business in Elane Photography case also raised religious objections, but the studio’s lawyers dropped that issue when they took the case to the Supreme Court. Instead, they argued that, since photography is a form of expression, the government should not be allowed to compel the use of that freedom in ways that the business owners find objectionable.
Whether that switch in the nature of the case played a role in the Supreme Court’s denial of review is unknown, except inside the Court; it customarily does not give reasons for such a denial. The New Mexico case involved a ruling that turning away a customer from access to a business open to the public based on the customer’s sexual identity violated the state’s law against discrimination based on sexual orientation.
This means we don't yet know if the Supreme Court would be open to the "it's my religious freedom as a business owner to refuse to do pictures or flowers for a same-sex wedding" argument, an argument that will almost certainly be brought to the Court in the near future. But in this case, the final answer is: No, Elane Photography (and other New Mexico businesses), you don't get to discriminate.