Exact same problem here.
There was an update the day before, saying it should fix this kind of problem (that never occured to me before).
And then, it happened to me last night. I was playing, and everything was fine. I came back in the evening and when I tried to start the game, it froze first on the white ''Minecraft'' screen, then I restarded after a moment, and since then it has not launched past the red Mojang loading screen.
Help would me appreciated here, because I spent too many hours on my world, and I would not lose all I did!
Thanks
PS4 / with disc. The bug started AFTER the hotfix (Version 2.09) for PlayStation 4 a few days ago (a fix for this problem.. which never occured to me before!)
Any clue?