1. Decide on the Group that is allowed to see the information - in this example I have chosen the group "Access to Private Addresses" and add the Users who are allowed to see the full Tax ID to that group:

2. Create a Custom View that masks the field for everyone.

3. Create a Custom View that unmasks the field for JUST  the  Users  in  the  Group,  adding  the  Group  on  the  "Access  Rights"  tab:

When Users not in the Group view the record:

When Users in the Group view the record: