Vladimir:
I suspect that few if any among us have examined our biases and hidden assumptions as thoroughly as we can, or ought to.
Fear, or conviction, stops us at some point, and we rest our arguments. That's the limit of anyone's competence.
As you suggest, relativity has physical, testable consequences. One realizes, as an observer, that what one observes is necessarily distant from its source, or else "The physical world is 'cock-a-doodle-do'" as Einstein put it. We assume that the distance has a limit, a point at which the world becomes objective, because we say that's what "objective" means.
Maybe, however, the world is too close to be objective.
Be well,
Tom