Strictly this is a bone of contention recognised and acknowledged by many physicists, including my professor on my General Relativity course. However, it is generally recognised that astronomy could not be considered science until it was fitted and explained within a Newtonian framework, justified experimentally on the Earth. The cosmological predictions correctly made by special relativity were certainly verified by astronomical observation, and “reasonably” it’s validity was acknowledged, even though later experimental tests more strictly confirmed its consequences.
Same goes for GR as far as it has been tested, but in so far as there is still doubt there is still debate. It probably doesn’t help that very few people in the world, myself included, understand GR[*-)]