Also, does no rewards impact gifts as well?

No, nobody can stop you from sending/receiving hive.

If you don't care about rewards, I would set the posts to burn, perhaps that will get you off the list, perhaps not.
BAW doesn't spend much time on the chain anymore, you might try mentioning him and asking.

You can post all the ai you want, provided you set rewards to burn.
This is well known in the hive, but you chose not to do that, and that may be what got you aded to the list in the first place.