The blogger Audacious Epigone had an interesting post on who commits adultery, based on the General Social Survey. The strongest variables he (?) could find were religious belief and political ideology. Taking just the ends of the spectrum, atheists were half again as likely to cheat as strong believers. Among men, the ratio is 30% to 20%; among women, 17% to 12%.
The gap was not quite as big between liberals and conservatives, but the former were about a third more likely to cheat than the latter. Among men the ratio is 26% to 19%; among women, 17% to 11%.
It is possible that the causation runs both ways. Cheating may lead people to become atheists and liberals. You can't really tell with GSS data. I have noticed in studies of pastors that those who end up divorced are also likely to become more liberal, whereas conservatives stay married (or marrieds stay conservative).
The direction of causation needs a longitudinal study.
I have read, though cannot tell from this survey, that secular conservatives -- that is, libertarians -- are the most likely to cheat, which makes sense ideologically.