You ask, "To what degree does the film's portrait of "violence" find confirmation in the text of Genesis? [and] To what degree are the movie makers distorting Genesis in order to falsely portray God and Noah as advocates of a "green agenda"? The first distortion worth mentioning is about something that is missing throughout the entire film.
Strangely, in this epic story nobody mentions "God" - not even Noah. Could there be a hidden agenda behind this film - write God out of the script?
Christians are not surprised that the account of Noah and the flood has been portrayed this way. We expect the Bible to be misrepresented and that every attempt will be made to shut God out. Noah only gets a hint from the Creator of the coming flood. Just as Monty Python’s Life of Brian pastiched the life of Christ, this Noah is falsely portrayed as a killer who is out to put a sword through anyone who happens to think too much.
Appallingly, the film has Noah misunderstanding things, thinking the Creator wants him to destroy all humanity, plus his own family. The idea of God regenerating an utterly evil and wicked society does not figure. But Noah is supposed to be guided by hallucinations induced by herbs, and to be in a surreal 'world'.
Equally unwarranted, unbiblical points are randomly inserted. No wives for Ham and Japheth; Methuselah is an esoteric medicine man; snakeskin being passed down through Noah’s family is supposedly important. As for the 'violence' part of the question, the Bible speaks clearly and unambiguously:
"The earth also was corrupt before God, and the earth was filled with
violence. And God looked upon the earth, and, behold, it was corrupt;
for all flesh had corrupted his way upon the earth." Genesis 6:11-13
Noah, however, was neither corrupt nor violent due to his great faith in God, and so "Noah found grace [favour] in the eyes of the Lord... Noah walked with God" (vss. 8 & 9) - this in contrast with the revulsion God felt at the rest of corrupted, violent humanity.
The suspicion that this film is not based on the Bible but upon Kabbalah – Jewish Gnosticism – seems warranted. The film seems designed to promote humanism, environmentalism, Gnosticism and vegetarianism, which will delight some people, no doubt, but avoids the real issues the book of Genesis shows as of vital importance – God will judge unrepentant evil-doers, but he shows grace to those who reverence Him. And Jesus spoke of the time before he returns to Earth as being like the days of Noah, particularly with people taking no note of God before destruction falls upon them. Mat. 24:36-44