Apologies in advance if this is a naive question. I'm learning the fundamentals of gravity and from what I've understood, it's not particularly meaningful to talk about it as a force, since it induces the same "acceleration" (classically speaking) in everything.
This means that whatever device or accelerometer we use, every component of that too will be accelerated the same way as the observer will, and the observer will not be able to measure (provided they or the measuring device are under no other influence other than gravity) any acceleration whatsoever. This makes it meaningless to talk about gravity-induced "acceleration" since we can't measure it.
One central idea underlying this is the equivalence principle (gravitational mass = inertial mass) that makes sense to me. But I wonder - is the fact that gravity acts on everything also fundamental to this? If there were anything at all that's not acted on by gravity, would the whole "gravity as a force doesn't make sense" premise (or maybe GR itself) break down? Is this question related to Mach's principle in any way?
(I'm not claiming any such thing might or should exist so please don't bash me for it - just trying to clarify my understanding)