GPS wouldn't work if relativity was wrong. Radio wouldn't work if our theory of electromagnetism was wrong. Satellites wouldn't stay in orbit if Newton was wrong. Modern medicine wouldn't work if our understanding of biology was wrong. And chemistry, physics, astronomy, mathematics and so forth all overlap, all require each other to some degree... and each of these interconnected areas of knowledge need to be correct, because we want to use it to build things or solve problems or make discoveries.
That's why I like science and engineering, it's a whole structure that, while not perfect or complete, has self-reinforcement and self-correction built in. And if it's right about something, the proof will be in the pudding. Otherwise, like you say, your airplane will fall out of the sky.
I believe you've got it backwards. The theory of relativity would be wrong if GPS did not work, the theory of electromagnetism would be wrong if radio did not work, etc. The only thing that working radio tells us is that certain mathematical model that we call theory of electromagnetism happens to agree with the real world (whatever that is) to a sufficient precision. For many purposes (like for example building radios), that is enough.
To a certain extent I agree, but I think you're missing a lot of nuance there. Boeing, for example, have built a lot of planes that fly as expected. The problem is the ones they built that don't: where bits fall off them or where their sensor systems don't work.
So do Boeing know a lot about aeronautical engineering, or are they just guessing? To what extent are they just pretending their planes are flying?
You cannot pretend it is flying when it isn't.
One of the reasons I chose to be an engineer.