Nintendo's version of the "Ubers" list can be summarized as "all mythicals (such as Mew), plus all species except Slaking and Regigigas who start out with a base stat total of 660 or higher, plus Cosmog and Cosmoem for some reason, and Necrozma/Zygarde who have non-mega form shifts above the forbidden threshold". For online competitions, the list also includes Ash-Greninja, but for Battle Tree purposes it doesn't, so you can use that just fine if you have one.
After you get more than 40 battles into a streak (or possibly even before then, if you get the extremely rare Anabel sighting), some of the teams you face will include the Tree-legal legendaries, and in fact many of the trainers are configured to have rosters full of nothing but legendaries. Your opponents will never use Tapus, UBs, or Silvally, but all the others that you're allowed to use, can also be used against you.