Hi Caro
I would say div school classes are definitely not - or at least not necessarily - from a religious perspective. Especially at schools like harvard and yale, the religion profs and classes are part of the university (and the religious studies depts), so the approach is academic. students come from a variety of backgrounds, so there is no presumption of being christian, etc. if you do an MDiv degre, which is more oriented towards ordination, those (mdiv-specific) classes and students might explore issues and scholarship from a more theologically oriented backrgound. of course there is a spectrum of approaches to the study of religion, from totally secular to very much from the perspective of a particular denomination or faith, and this manifests differently in each scholar, student, publication, class, etc. in all, though, at many divinity schools, the classes are academic and do not presume any religious background. of course a seminary, and perhaps the divinity schools of more conservative or church-oriented schools, will have more of a religious perspective for classes
i went to harvard div (mts), which is part and parcel of the university at large - many of the classes are attended by students of GSAS who are not from the div school, and you can attend classes offered anywhere in the university (especially NELC, archaeology, etc., but including any subject). like i said, the mdiv classes are more theologically oriented, and while the div school is a great community and offers various religious events, many of the students and profs are secular, and most of the classes are 'secular' inasmuch as they approach the subjects academically, and not from the perspective of a believer. i believe the GRE is not required for the mts/mdiv applications, so you could try one of those programs and see how you like it. i thought the div school was a fantastic environment, and harvard of course a very resource-rich place to study.
hope that helps!