Are any of the quests in Horizon: Zero Dawn time sensitive?

There are no time-sensitive quests in the game. There also isn't a real "point of no return" for the side quests, after you finish the game your game is reset to the point before the final mission and you can continue to explore and do sidequests.

There is a point where the game warns you to finish any unfinished tasks, but that only means that you are about to do a pretty long quest that you can't leave until you finished it.

There is an order to the three main quest series, if you do them out of order at some point one quest line will pause until you have done some of the other main quest lines.