Ultimately fans want to see the characters they grew up with on screen, both personality and looks-wise, the story can come second (in terms of comic-accuracy). That's what MCU movies have over X-Men. Yes Singer has love for the X-Men, but he has reimagined certain characters to fit his vision, and that's what fans don't like, and what indicates that his love doesn't extend beyond some characters.
Like Rogue... OT Mystique (looks-wise, but I love that look)... FC Mystique (only exception being her Saigon scene in DOFP, otherwise very much unlike the comic book character)... Storm (although the casting is the root problem; her scene when she rises up from the elevator and eletrocutes Toad, and her scene in Cerebro 2.0 against Jason Stryker being exceptions)... Iceman... Cyclops (although he was OK in X1, it is strange why he shafted him in X2, and while he treated him well in XMA, it can be chalked up more to the pressure of fan complaints about him than Singer liking the character)... Banshee... Havok... Moira...
The ones I find accurate are Magneto... Charles... Wolverine... Jean Grey... Nightcrawler... Sabretooth looks-wise, but he was a mute... Psylocke looks-wise, but we get no insight into her character, anyway the list isn't long, Beast's origin and intellect seems accurate, but his personality not so much.
On the other hand some things weren't that accurate but were done greatly... like Stryker... the Sentinels... Another strange case for me is Emma Frost, IMO she wasn't badly written, she was Shaw's right hand henchwoman like in the TAS Dark Phoenix episodes, the problem is 1) the actress and 2) the fact they had no plan to use her afterwards.
And to be fair with both Kinberg being a Magneto fanboy and Singer being a Charles fanboy, it is not hard to see why those two have been favored both in original trilogy and in prequels. Why did they never get someone who was passionate about comic Storm, comic Cyclops, comic Mystique, comic Rogue, etc to direct or write these movies? Anyway, sorry for the long analysis.