Okay, so I realized that the custom fields are showing up on the edit page for the custom post type for non-admins, but not when they’re initially creating the post. If they save the post as a draft or publish it, then the custom fields will display.
I don’t think this problem has to do with the theme or plugins. I tried changing the theme and deactivating everything, but the problem was still happening. I also tried creating a new custom post type, and the issue was still occurring for non-admins.
Any reason why it’d be doing this?