There is no law in the United States that treats gays and straights differently.
What is conservative about the government regulating what two people do in their own home?
You're confusing conservatism with libertarianism. The US since its inception has had laws regulating sexual behavior. Conservatism says don't change those laws without good reason to expect doing so will improve society. Libertarianism says such laws are ideologically unsound.
That is certainly not true. I'll give you two examples from the many available.
First, Nebraska has a hate crimes law that treats gay victims differently from straight victims.
Second, the U.S. has the famous "Don't Ask, Don't Tell" law that expels gays from the military. Under that law, if a gay persons says that he is gay, then he is expelled from the military. But if a straight person (poor Klinger from M.A.S.H.!) says that he is gay, he is not expelled. Just saying that you are gay is not enough to get expelled. You actually have to be found to be gay, even if you have never engaged nor ever intend to engage in homosexual activities.