The classic case is the "The Life and Voyages of Christopher Columbus" where it was claimed he was aiming to prove the Earth was not flat. My personal peeve is movies like "The Imitation Game".

Biopics/dramatizations of events often bring multiple minor characters together into a single person.

I would be more bothered by the change of small details irrelevant to the narrative than I am by larger character changes. I would prefer that the mainline details stay the same - chain of events, impact to the town, aftermath - but I am not watching the series in order to write a paper. I appreciate the articles which document the fiction vs. reality of historical dramas, but I do not share in any anger. Then again, I'm not related to anyone whose character was represented in the series.