You do not have a "right" to tax money
The case before the Supreme Court over federal funding for fighting AIDS is a perfect example of how we have a warped understanding of "rights" in this nation.
First, let's establish what true rights are: Something that requires restraint by the government and does not require anything of anyone else. No one has to spend a penny for me to have the right to free speech, the right to be secure against unreasonable searches, or the right to not be deprived of my liberty or property without due process. If the thing I want requires someone else pay for it, then it is not a right.
Basically, a requirement of getting a grant from the federal government to fight AIDS is dependent on certain preconditions. This is boringly normal across all levels of government and among private sector organizations. If you want financial help for something, then you have to agree to certain things to get the money. This is the case for things from fighting AIDS to grants to local charities by city and county government.
So, does a private charity not want to take a position against prostitution? Fine. You do not have to take the money. If you do not take the money, you can run your organization however you like, whether or not you agree with federal policy. With government money comes government strings, and when you take the money you agree to be bound by the strings. There is no free speech issue here.