See, that's the thing. They think they are on Christ's side (or he's on their side). The Bible is the absolute word of God, so they think there's a divine mandate to kill the gays and, if the trinity thing means Jesus = God, the divine mandate from Christ is to kill the gays.
Also gay sex is icky to them, so there's an extra bit to justify killing the gays.
Honestly, I'm surprised that we haven't seen a Spanish-Inquisition on this yet, but I'm sure Republicans are working up to it.
I'd rather have a dysfunctional government than a malicious government.