Rona,

You may be able to expand upon Jacob's initial suggestion by replacing the logic that checks for the org name with code that looks at organization tags. The below snippet should go through all of the users's organizations and if it doesn't see the tag that you want to filter from, it will hide the form from the users that lack the tag.

    for (var c in HelpCenter.user.organizations) {
      if (!HelpCenter.user.organizations[c].tags.includes("YOUR_ORG_TAG")){
         $("#TICKET_FORM_ID").hide();
      }

I haven't verified this one, but I would suggest checking the comments on the linked page as there are some other related solutions that might help land on the right solution for you as well.