I've noticed that both sides of my family have both told me on separate occasions to not have the soles of my shoes facing upwards. Is it some religious thing, b/c either side follow different faiths, or a cultural thing?
Soles of feet and shoes are considered "unclean" and thus, taboo in many cultures, independently from one another.
A simpliest hypothesis to explain that, is than in pre-modern cultures, one's shoes and feet would often be smeared with manure, muck or mud, and thus, pointing them to someone was considered offensive and disgusting. This is supported by another cultural aspect, that in many cultures (from Arab to Japanese, and even Slavic) it is considered rude and barbaric to walk around the house in the same shoes you use while outside, and most of those cultures offer slippers to guests. It is also partially expressed in the New Testament, where wiping your shoes on someone doorstep is a sign that you have no respect for them, and are done with interracting with them.
Moreover, shoes are considered so unclean, that in many cultures it is unacceptable to ever put shoes on the table, even if these shoes are brand new and never been worn.
In Europe, it also plays into a curious cultural quirk, that pre-XVIII century it was common for people to insult one another by exposing nude crotch or buttocks to one another, also do to percieved "dirtiness".
source:
A. Blausch "the history and form of medieval shoes" 2012