Tom Rees has a blog post, Religion and marital infidelity, which shows that religious attendance, but not belief, correlate with a tendency to not have affairs. I think the critical point here is that religion is a complex phenomenon, and we condense many separate dimensions or parameters into one term. For example, there seems to be a tendency with higher socioeconomic status to be positively associated with religious attendance and affiliation, but negatively associated with religious beliefs.
There are so many possible directions for causality to run in something like this that it is hard to suss out what the raw facts might mean. For example, church attendance tends to be a familial activity, and so perhaps that declines in some fraction of marriages where one or both partners are unhappy, prior to or along with infidelity. This would be a cause that has nothing to do with religion at all. Does GSS ask how many cocktail parties its respondents attended the previous year? That might be negatively correlated with infidelity in the same fashion!
From my observations, wives largely control religiosity. Wives most often select the religion and habits of church attendance for the family. This is true when relationships are stable, but when things go sour, habits change.
When women have problems with their husbands, they often go to church. When men have problems with their wives, they often go to a bar. Hence men attending church is a sign of marital stability - or exceptional tolerance. I also believe that there are more single women who attend church than single men.
Shoot, people talk, and church-goers tend to run in small social communities that are not immune from gossip. The porous social network itself seems like a good deterrent to extra-marital affairs among men (and women), particularly when church norms harshly judge affairs, and males have a lot to lose in terms of social status in their community when they are expected to engage in weekly public events. Game theory models of "cheating" (not in the infidelity sense) show that rapid communication among interactants is a major deterrent to the spread of defectors. Just a thought.
If they're going to church all the time, how can they have any time to have an affair.
I agree, with Rich. It's about shame within the social circle. Regular attendees will be a part of a social set and will not want to lose status due to breaking the rules.
Here's my explanation:
Those who go to church on a regular basis do so because they believe they are supposed to do so. As in...they are *required* to do so, by God. And this same "do what you're supposed to do" belief system is very likely to translate to staying married as well--not as a choice or a preference, but as a function of the believer's moral identity.
In other words, they'd maybe "like" to get a divorce, or maybe "like" to take a few days off of going to church, but they can't do either because they're not supposed to.
On the whole, I'd say it's doing something positive for the wrong reasons.