Want to display in a profile that a particular contact is part of a smart group related to their membership type
If you are using Drupal, why not make a Views Block showing membership status/type and put this somewhere eg /user?

I understand I am not answering the OP of 'how to show a Smart Group in a profile' but am trying to answer a more generic question "how can i show a user their membership type"

You may find a downloadable view that already does this in our Treasure Trove eg this one