Spurred by Sgt Joe Friday, I used the GSS to take a look at what percentage of self-identified firm theists do not attend religious services with any regularity (defined as going less frequently than once a month). He expressed surprise at how many on the right still attend churches that increasingly incorporate leftist causes (ie, environmentalism and open borders) into their services.
To some extent, the political alliance between pious Christians and the GOP is a consequence of the latter welcoming the former while over the last few decades the Democratic party has come to be seen as increasingly inhospitable to many believers, especially white Protestant evangelicals, more than it being a result of these pious Christians sharing Rand Paul's views on taxation and government regulation of private enterprise. As long as SWPL views on deeply held Christian faith (among whites, anyway) remain disdainful, there will be a sizable contingent of white evangelicals who stick with the GOP even though their political beliefs aren't particularly rightist.
Anyhow, considering only responses from this millennium for contemporary relevance, we find that 39.5% of firm believers show up less than once a month, and 17.9% don't even make it on Christmas. Among conservatives, the figures are 28.4% and 11.8%, respectively. For moderates, 44.9% and 21.0%. And for liberals, 50.1% and 24.3%. A quarter of conservative believers and half of liberal believers don't go to church.
GSS variables used: POLVIEWS(1-3)(4)(5-7), GOD(6), ATTEND(0-3)