I'm pretty sure Ryanair is not the only operator flying non Schengen flights into BUD. Are those other operators subject to this border control ?
Yes.
Many times I have had to get out with half the crew, get a bus, and have my passport inspected. Then we go back and the bus does the other half of the crew.
We complained, grumbled and said that it was not needed anywhere else. But in the end our lot just re-scheduled to include a longer turn. In fact, I think that the route has now been pulled altogether, but I could be wrong (just not done it for a while).