This could have something to do with the permissions set up for the post type in the theme, I think I remember something in the past similar to this. Unfortunately, I can’t really test this and I don’t remember what the solution was.
Here are a couple related topics (it seems that a pre_get_posts filter not done correctly could also do this) https://support.advancedcustomfields.com/forums/topic/custom-fields-not-showing-for-non-admin/, https://support.advancedcustomfields.com/forums/topic/acf-fields-not-showing-for-wp-membership-groups/
Have you tried using a different theme and testing to see if non-admin users can see field groups?
