Does the main story matter in open world games?

[TheWPCTraveler]

It really, really depends on which is better.

If the story is good, but the side quests are meh, I'll probably soldier on through the game and hope it gets better. This kind of stuff makes the gameplay look bad to me.
If the side quests are good, but the story is meh, I'll tune out on the story. Plain and simple. If the story is bad enough, I'll drop the game, but I have low standards.

Now, if there's a big disconnect between the gameplay and story...I'll drop it.