Were you able to resolve your issue? I just tested it and it works for me.
Reproduction steps:
- create user field using multiselect as the field type, editable after signup, show on public profile, show on user card, searchable
- edit a user to choose one or more items from the multiselect and save changes
- look at user profile and user card to confirm the multiselect items show up
- use site search to search for multiselect items and confirm the user shows up