So the desire to win at any price means the Republicans have to become Democrats?
No. The RINOs who take that route use the target-groups' "victim mentality" as a lever to political power, the same way as the Democrats do.
What Republicans need to do is work to break the victim mentality that the Democrats have so adeptly forged over the years. They also need to steer a narrow course between the left's outright promotion of homosexuality and the hard-right's efforts to use the fist of government to totally squash it.
Consider this: if asked whether schoolboys should be given explicit instruction in how to perform e.g. anal sodomy and should be encouraged to try it, the vast majority of Americans would say no.
If asked whether gays should be allowed to have open sex in a public park, the vast majority of Americans would say no.
On the other hand, if asked whether the government should have the authority to wiretap a motel room on the suspicion that two gay men might be "getting together" there, and to arrest the men for their private actions, the vast majority of Americans would say no to that as well. Note that even those Americans who would never dream of partaking in such rendez-vous themsleves may be bothered by the nosiness entailed in the government's actions.
In the first two cases, most Americans side with the Republican view. In the last case, they don't. While Republicans should stand for principles, they should also recognize when issues have multiple sub-issues which demand different treatment.
On a parting note, Republicans might do well to consider the bumper sticker, "Gays with guns don't get bashed." Encouraging homosexuals to arm themselves against people who would unlawfully batter them is apt to be a good way to throw liberals into a tiz. It attacks gays' "victim mentality" by offering them a solution to one of their problems which is far more effective than any "hate crime" statutes the Democrats can offer. Further, it puts Democrats on the defensive on RKBA issues; if they oppose letting gays arm themselves, then it exposes them as not being the frinds they claim to be.