Well, user meta is entirely different than taxonomies. If you mean user meta in the more general sense where user related data is somehow managed through taxonomies, then the default taxonomies require manage_terms
capabilities. However, with custom taxonomies, you can specify special capability names for various actions when the taxonomy is defined. Then you can selectively assign such capabilities to roles or users.
User meta as it pertains to WP, is specifically user related data that is stored in the usermeta table. By default, there is no way to add more user meta through the admin screens. Any additional meta would need to be managed through custom code, which of course could include any sort of custom capabilities you might conceive of.
I would suggest you abandon trying to use the built in post taxonomies for users and create a similar system using using usermeta to store the information. It doesn’t need to be as elaborate as post taxonomies, perhaps simply storing an array of assigned user tags in postmeta will suffice. Only those with some custom capability would be able to edit these.
If you will be needing to do user queries based on these assigned tags, you should store the tags under individual keys instead of in an array. User meta queries restricted by array content are problematic to set up.