I have attended numerous Republican caucuses and conventions, sometimes as a delegate, and sometimes as staff. What really bothers me about the conservative/moderate label is that the majority of the "religious right" are not conservative at all. They are anti-abortion democrats.
If the democrats were to change their position on abortion (which is *not* happening), the "religious right" would abandon the Republican Party in droves. I have seen numerous instances where the "religious right" has supported a democrat over a Republican because the D was pro-life, and the R was pro-choice, even in a race where the office holder would not be in a position to have any effect on the issue. They are not Republican, and they are not conservative.
More specifically, anti-abortion populists, in the Huey Long mode. About one-fourth of a generation away from Jim Crow. Anti free trade. Theocrats.
The tent bulges and the mind boggles.