They’re like wyverns in many ways, one of which being that most nothing will attack them whilst riding unless provoked. (With the exception of Nameless and Reapers, because they’re bastards). However, something important to note is that if you have a second passenger (since the saddle is a two seater) anything aggressive that wouldn’t agro on you before — now will. Not sure if this is a bug or what, but the passenger can also get hurt, so be careful.
Good luck out there, survivors.