It's bothersome for two reasons: 1) The true story is usually compelling enough anyway; and 2) these movies have become a vehicle for teaching history, which means it's being taught wrong.
I'm one of the people who, immediately after watching a movie "based on a true story," seeks out the fact-vs.-fiction writeup so I know how to sort it out. The only thing that bothers me anymore is the demonizing of people for cinematic purposes. Was it necessary in "Selma" to paint LBJ as anti-progress and an enemy of king? Or in "The Express" to assign West Virginia fans the most racist caricature, when Ernie Davis never even played a game at West Virginia? Or to have Hurricane Carter unjustly lose to Joey Giardello (who is portrayed as the beneficiary of a fix) when every account of the fight from that era agreed that Giardello destroyed Carter?
I understand condensing characters and eliminating extraneous storylines. I don't understand making stuff up to make real people look bad.