They have good reason to nor respect or trust Jon, he's got a lousy track record as a leader:
His first leadership role was Leader of the Night's Watch -- some of his men murdered him, that's how much they trusted his leadership.
His near-disastrous leadership in the Battle of the Bastards has already been discussed at length.
When the Northmen acclaimed Jon King of the North, he immediately left for months, then returned having given up his title to follow a foreigner who was a descendant of the hated Mad King ... without consulting anyone.
He comes back and just expects everyone to accept and support his actions, including Sansa, who's been working hard at keeping the North in line during his absence. I don't blame her for being pissed, she was holding Winterfell for the King of the North, not for the Consort to the Queen.
In other words, every time Jon's been in charge, he's either failed or had to be saved by someone else (sometimes by magical means). Jon's a noble warrior and a good man, but he's a LOUSY leader.