You can ignore them if you want, or grab them while you do the story in the season if you want. I've leveled a couple of alts to the nightmare dungeon stage, and with some of them, I haven't touched a single side quest. I do world events and dungeons to level. On other alts, I'll do side quests if I happen to see one, or I'll pick it up from the quest giver and if I happen to be near the objective, I'll do it.

Seasona reset everything every time they start (except this first one where they're keeping some of the world stuff). You can do the reset stuff, or not. It's up to you. But I wouldn't quit over it because it's not really required.