Cobain's political/cultural writings of the early 90s absolutely fit the modern SJW and gender ideology of 2021 to a T. If he were born 30 years later he's the exact kind of guy who would end up trooning out. That said, in the alternate universe where he didn't eat a shotgun, I have a hunch he would have eventually grown out of that long before the trans shit became mainstream enough for him to actually transition.
Also, you just need to look at someone like John Lydon, Morrissey or Kanye to see how musicians that were once seen as left-wing in their heyday can slowly shift across the spectrum. Who's to say Kurt wouldn't have somehow ended up becoming an epic Trumptard had he lived to 2016? Most people in the music business are just generic anti-establishmentarians and will latch on to different ideas they feel are going against the grain, at different times.