I agree with that for the most part, I don't agree that MOST moderates vote republican, but definately quite more than vote democrat. The problem is that the republican party has mostly forgotten about conservatism (that is a truly conservative view on government), which is what initially endeared the republican party to moderates.
Moderates want to be left alone, but are willing to make reasonable concessions to keep things running and to keep themselves and their communities nice and safe. This is what the republican party USED to stand for. Through it's increased peddling to the religious right (who themselves are powerful through being disliked less than the hardcore secularists), and in making that the cornerstone of their domestic policy, at least publicly (supporting economic views that people who dislike their social plans less than the liberal ones will be left saying "Alright, I'll take your word for it"), they've forgotten about keeping government for the most part out of our lives and keeping our neighborhoods nice and safe. And thus why the republicans are genericly quite a bit less popular than the democrats.
Yeah, by and large people don't like the idea of gay marriage or abortion. By and large people think there should be some restrictions on abortion. By and large people don't like the idea of pornography on network television, or rich hollywood folk who don't do any real work telling them how to live. But this does not mean they believe that the gays are subverting society, or that women having abortion should be jailed, or that we should only have "7th Heaven" reruns on, or whatever. And that's the problem with the republicans, the extremists have them by the balls, and by this point most of the republicans holding office now are extremists themselves, and thus they will be punished.
I was a registered republican for 3 years, I led a recruitment team.