i think it is just mostly axl rose being his typical beep self

Thats actually a bit incorrect.
The feud took place before that fight happened. That's why Axl walked over to them so pissed off. Because they publicly bashed him a number of times and Kurt refused to tour with him.
And the hat he wore in the video was also done before the feud. It was back when Axl was openly praising Nirvana and wore the hat as a fan to support the band. Only then Kurt refused to tour with them when he was asked and Axl got dissed.

It's actually a much better story.
Courtney was out of it and started hassling Axle Rose at the VMA's. She claimed that she wanted Axle to be her baby's (Frances) Godfather. Axle got in Kurt's face and said "You need to tell your B!tch to shut her mouth", Kurt got right back in Axle's face, turned to Courtney and said "B!tch, shut your mouth", with a grin. Axle chuckled and walked away. To show appreciation, Axle wore a Nirvana hat in the "Don't Cry" video (if memory serves).

Personal.
Axl loved Nirvana's album 'Nevermind' and asked them to go on tour with Guns N Roses. Kurt turned down the offer and said it was because he hated Axl for being racist, homophobic, abusive to women and sexist. Axl got angry that Kurt was bashing him in the press and that he rejected his offer to open for them, and the feud took off.

This message has been deleted.