Specifically, I'm wondering how the state propaganda/funding may have affected academic research. A reasonable hypothesis is that the officially atheist Soviet financiers would be interested in funding (e.g.) archeological digs that might disprove the historicity of biblical accounts. Or maybe no one in Soviet-bloc countries were even interested in biblical research, and so none was done. Or maybe politics had almost no influence, and the major differences were due to the pre-existing theological split between the Orthodox and Catholic/Protestant churches.
I previously asked this question on /r/AcademicBiblical with no response: https://www.reddit.com/r/AcademicBiblical/comments/7xt3ti/how_did_the_cold_war_affect_academic_biblical/
Hopefully, this is an acceptable comment since it doesn't directly answer your very interesting question.
A new subreddit has opened up recently that, currently, has 38 'approved scholars' that may be able to help answer this question.
How about submitting this question to them at /r/AskBibleScholars?