I haven't investigated it very much. But it's an option AFAIK in the vBulletin forum software. I haven't seen any need for it so far. But the listing of it in member's profiles is by default. Not to say it won't be investigated further in future. Definitions of "public" group would need to be agreed to. We currently have a limited no. of groups of members.

Depending upon how the forums develop, there's a chance for such an option. But, as suggested earlier.