Would it be possible to EXCLUDE some assets from showing up eg groupjive.groups.[xyz].activity.[activity_id].tag?
No, not at this time. An exclude parameter is planned for a future release.
The reason is that it is now showing up twice. Once as the activity in which the tag has happened and once as the activity tag that has been produced because the activity has been tagged.
It should group the activity together. Is this happening after your asset change or before it as well? If only after your change then that's to be expected as you changed the asset to something not officially supported or tested.