World Without End (1956) on Netflix

Returning from the first manned mission to Mars, a crew of American astronauts find themselves in for a very rough ride when their craft comes into contact with a cosmic anomaly that causes the ship to reach a tremendous speed. When they crash land, they're not quite sure where they are. They soon find a graveyard that confirms they're on Earth - but far into the future. An atomic war has destroyed much of humankind and the four astronauts are attacked by mutants. They escape into a cave and are rescued by a community of humans who have made a life for themselves underground. They are made welcome but one of leaders of the underground civilization sees them as a risk to his ambitions and sets about to have them banished.