Okay, first:
Second,
If the Republicans court homosexuals, as you say they should, they might gain a couple votes, but they will lose a massive amount from it's right-wing base, it's evangelical base, it's bread and butter.
I, in fact, will leave the GOP party if they start courting gays, lesbians, bisexuals, and transsexuals. I imagine many others will follow suit. The trade off isn't worth it for the GOP.
Toning down the ridiculous, backwards, homophobic rhetoric isn't just about getting gays to vote for them. There are a lot of straight people in swing states (like me) who think Republicans are 50 years behind the times on this issue. So while Republicans will lose people like you, they will probably gain back upper-middle class educated voters who left the party 10 years ago but don't want to pay high taxes. Winning hate-mongers hasn't really worked out for the GOP the last few Presidential election cycles.