Personally, I usually look at a movie if it works as a movie first. If it doesn't, then all the accuracy in the world doesn't guarantee my liking it; if it does, that goes a long way towards my forgiving its inaccuracies.
So it's more of a case-to-case basis for me. Troy is so bad it's not even worth discussing; The Quiet American has good things, flawed things in it; Gibson's movie upends the message of Christ to the point that it's a Mel Gibson movie (pain and not love will set you free) and anti-Jewish. Birth of a Nation and Triumph of the Will I can appreciate as great filmmaking the same time I appreciate that they are gross and horrendous distortions of of history (Gibson's movie is also a gross distortion; difference is, it's not even good). There's no simple answer.