The arrival of the Brotherhood of Steel's Vertibirds and infantry is essentially inevitable, unless you plan to forgo most of the main storyline. According to Nukapedia, this occurs at the end of the Reunions quest.
There does appear to be a bug that can be triggered by the player, which would prevent this from happening. However, it may be patched at a later date as it can break some portions of the game - especially for players who actually want to side with the BoS.
Bug details, from the aforementioned page on Nukapedia:
The Prydwen and BoS vertibirds will only appear if the player character exits Fort Hagen via the rooftop access elevator. If the player character exits the area by backtracking their steps, it will present a "bug" in which the BoS have not entered the Commonwealth, and NPCs in Diamond city will comment on the "Blimp" being at the airport and such but it won't be accessible. To fix this, simply travel back to the Fort and leave the building via the elevator to the roof as intended.
As for getting rid of them after they've arrived, the only plausible option seems to be following any of the non-BoS main quest branches to their conclusion or near-conclusion. However, I have not found reliable documentation (and anecdotes I've seen vary) to confirm whether this is effective or if there are any bugs which may keep the BoS around past the point where they logically should not be.
I'm still working on my first playthrough, and I plan on finishing with one of the non-BoS groups. I'll try to come back and update this with details of my experience once that's done.
Also of note: You may not be losing as much XP as you think while the Brotherhood wipes out enemies for you, if you're losing any at all. Several times, I've noticed the "cha-ching" sound and an XP boost being triggered while I'm out and about - despite me having done nothing at all to earn it, and being nowhere near the combat zone. This usually happens shortly after a Vertibird flys by and/or I hear explosions or gunfights in the far distance, indicating the Brotherhood is hard at work somewhere. So, it seems the player may earn at least partial XP from the Brotherhood's kills.