This really isn’t even a theoretical discussion. Some social conservatives do make public-health arguments in favor of legally discouraging homosexuality, citing STD statistics. Even consensual gay sex was once prohibited through sodomy laws in every state, albeit usually on moral grounds. The last of these state laws were struck down by the Supreme Court in 2003’s Lawrence v. Texas.
The point isn’t that there aren’t any relevant distinctions that can be made between various behaviors or the effectiveness and fairness of trying to ban them. It’s simply that liberals and conservatives alike should learn to be more careful about giving the government powers they aren’t going to want to see exercised when the other side is in charge.