Well, NASA trusts Linux enough to send it to Mars. They build rockets, so it should be good enough for flying busses. Unless you don't trust your software engineers, but then having them build a custom microkernel OS instead sounds not much better.
Every NASA crewed launch to ISS from US soil is on a stack that uses Linux for avionics: Falcon 9 and Dragon 2. The Starlink constellation is also a massive deployment of Linux nodes in space.
The backup NASA commercial crew system from the 737 Max people hasn't flown people yet and probably won't this year, perhaps never. They somehow managed to have two critical software failures on their first orbital flight test, either of which would have caused loss of vehicle without intervention. Both should have been caught with comprehensive testing.