The ending was really sad. I'll never ask anyone to hold the door for me again.

If I understand correctly: Bran was controlling the adult Hodor using his abilities as a warg, but he was simultaneously using the Sight to view a time far in the past. Most of the scenes this season have had the common thread that using the Sight allows the seer to actually interact with what he is seeing. So while he is viewing the distant past, he is also present and seeing through the eyes of Hodor at the moment of Hodor's own death. The young Wylis notices Bran, and upon locking eyes a connection is formed through Bran to his adult self as he desperately tries to hold back an unfathomable horror by 'holding the door'.

For the young stable boy, who has to this point lived an unremarkable life, suddenly experiencing with all of his senses his own inexplicable death as the life is choked out of him by the same dessicated, animate cadavers he is trying to brace the door against, it proves too much for his mind to process and something breaks inside of him. He collapses in a seizure as he repeats over and over the command running through his adult mind in his last, desperate minute. "Hold the door! Hold the door! Hodor!"

What we've seen so far indicates GOT is set on a single timeline. This means anything Bran changes in the past has already happened. So he could theoretically be responsible for the death of someone who is already dead, but he can't go back in time and murder someone - else they'd be dead before he did so. If he kills the night King it would have to be in the present.

Additionally, Bran might have realized what was happening. He was affecting the young Wylis, but he simply did not posess the finesse with his warg abilities to be able to release his harmful interference on Wylis without also severing his connection with Hodor, who might have slackened his hold on the door in his confusion.

An event occurred in the future which interfered with the past, causing the event to happen in the first place. Bran seems to have closed his first paradoxical, yet stable loop in time.

In short, everything is set in stone no matter what Bran does. Whatever happens was meant to happen.