Well that depends on where the back story came from. If it came from the TV shows fine. If it came from the RPG material, the Techmanuals or the Novels then it's best to leave it out. If it's some supposition or contecture that never made it into any story, or was in fanfic then hell no out it goes.^ Which fans? Different people have different ideas of what Star Trek is or should be. There have been five different Trek TV shows that someone will call their favorite.
The whiners here who bitch and moan the same song and dance with every post think they're the one true fanbase who knows what Star Trek is all about. Hell, some of those crybabies will watch this movie more times than anyone here who loves it just so they can tell us how right they were!
I'm not denying that...I'm just suggesting that "you dance with the date that brung ya", as it were.
Would it have been that hard to write their story keeping the facts of the various characters' back stories straight? Would it have hurt to keep their PERSONALITIES straight? (Kirk may be a womanizer, but a pawing letch?) Would it have hurt to stay closer to the original sets and ship design?
If you can have BOTH sets of fans happy, why not try for that? To dismiss ALL of them just because a few of them are a little obsessive seems to be to be unecessary disrespect for those whose dollars for 4 decades have kept this franchise alive.
There is such a thing as "middle ground" here, but people don't want to see that (on BOTH sides).
BTW a great man once said "You can't please everyone."