Does the right to free speech apply to policy positions taken by groups which receive federal money?

The Supreme Court has agreed to hear a case challenging a 2003 law that "requires private groups that receive federal money to combat AIDS abroad to have 'a policy explicitly opposing prostitution.'” The case is United States Agency for International Development v. Alliance for Open Society International.

From the NYT:

In 2011, a divided three-judge panel of the United States Court of Appeals for the Second Circuit, in New York, blocked the law, saying it “compels grantees to espouse the government’s position on a controversial issue.” The full appeals court declined to rehear the case. Dissenting from that ruling, Judge José A. Cabranes wrote that the measure was “an uncomplicated and common-sensical condition of federal funding.”

In 2007, considering an earlier version of the program, the United States Court of Appeals for the District of Columbia Circuit upheld it. The federal government asked the Supreme Court to hear the case from New York to resolve the conflict.

In urging the Supreme Court not to hear the case, the groups challenging the law said it interfered with their work. They said they “generally avoid taking policy positions or making statements that are likely to offend” the nations they work in and the people they seek to help. “Adopting a policy that explicitly opposes prostitution” would do harm to the groups’ “effectiveness in working with high-risk groups to fight H.I.V./AIDS,” their brief said.