To what extent do the religious beliefs of an author affect a paper's chance of being accepted? Implicit gender bias is present in academia (at least in the sciences). I've heard that some journals hardly accept any manuscripts written by Muslims. To what extent do the religious beliefs of an author affect their paper's chance of being accepted? Have there been any studies that look at implicit religious biases?
In my entire scientific career, I have seen religious belief come up precisely once: an (apparently Christian) author closed a paper with "AMDG," which apparently stands for Ad maiorem Dei gloriam.  Of the set of three peer reviewers, one ignored it, one was confused by it, and one asked for it to be deleted as irrelevant to the substance of the paper.  The authors removed the acronym as part of their revision (amongst other changes) and the paper was published.

The other place that I know that religion comes into play in scientific publication (though I have not personally encountered it), is when a person attempts to use statements from their religion as evidence for a position.  This never goes well: in a scientific context, claiming "the Bible says ..." or "the Koran says ..." is equivalent to saying "The Lord of the Rings says ..." or "Fifty Shades of Grey says ..."  Such a document is a secondary source at best, and one that has no particular reason to be regarded as a reliable source of evidence, despite the magnitude of cultural belief.  Such books can, of course, be cited and analyzed just as any other literary/historical work, but that is different than using them as evidence for a scientific position.

So, in short: if you don't make your religion an issue in your manuscript, it should never come up as an issue in the normal scientific publication process.  This doesn't mean you might not encounter horrible and inappropriate behavior (scientists are just as capable of being terrible people as anybody else) but it is definitely outside the norm of the peer review and publication process.