The so called religious right is not exactly what a lot of people think it is.
First off the only really active portion of it is the evangelicals and they don't have any real large numbers compared to other special interest groups at least when looking at the overall party membership.
Secondly...just like in any party....it doesn't and cannot exert the same kind of control that far more numerous and larger contributors do (corporations and extremely wealthy individuals with corporate interests) so much as it appeals to the spurious perception that if you don't wave your religious flag (at least during the primary) the republican voters wont elect you, which is a blatant attempt to tie their special interest (the promotion that religion, and in particular WASP..white Anglo-Saxon protestant religion) is somehow synominis with being a conservative. Which is basically false advertising on its part and a poor use of sophistry especially since it couldn't be farther from the true demographics of the party.