I'm using a shop mod that just uses player heads as the "shop", and everything I've tried doesn't let non-allies interact with them. Here's the link to the other mod in question. What can I do to fix this?

https://modrinth.com/mod/universal-shops

I don't think they're using player heads on the server side, it's an actual block, so the block ID you should be adding is different.

you just need to add the block bypass with these things
"universal_shops:trade_block"
"universal_shops:admin_trade_block"
worked for me