I am specifically interested in Greek and Roman paganism: the gods and the customs and festivals honoring or surrounding them. Even though people weren't necessarily outright worshipping them during the Middle Ages, could their presence still be felt in Christianity at all?
This is quite frankly a ridiculously broad topic. Are there any specific areas that you're interested in?
The absorption of indigenous religious traditions into Christianity was after all not a uniform practice and the experiences of the Mexica were quite different from the experiences of the Norse who were in turn different from the neo-Platonists and so on.
you might want to check out some of the existing material from the wiki
https://www.reddit.com/r/AskHistorians/wiki/faq/religion#wiki_christianity
under
Non-Abrahamic Influences on Christianity