How can one become a very good chess player without studying chess or openings? I heard that Capablanca never liked to bother with openings, would never study chess or read books. Despite all this, he became world champion. Is this an exception to the rule?  Have times changed today were players are too strong and study is mandatory?
Capablanca didn't like to "study chess or openings" means that he didn't like to study formal chess (as it was understood in his time).

On the other hand, he studied more, and had a better grasp of chess principles, particularly as they related to the middle and end game. His best exposition of this was "Chess Fundamentals."

Because he focused on principles, rather than "book" moves, he was the hardest person in the world to surprise with a new line. He beat back the Marshall Attack that Marshall had reserved especially for him.

Nowadays, there is more and better book knowledge, so it's helpful to learn some of it. And the other reason is that not many players have the instinctive grasp of the game that Capablanca had.