Galadriel tried to stop the Kinslaying - it's the reason she had to cross the Arctic rather than ride on ships[1] - and she didn't "run away" from the War of Wrath. As for her general character, though she was proud and wanted to be "free" in her own lands, she was described as wise, understanding, and merciful from her earliest years. [2]
I am never going to watch the series because the movies were bad enough, and I find it cringe-inducing how people talk about "the lore" and act as though adaptation can occur 1:1 from books to video, but I have found people seem to be spreading and repeating a lot of misinformation apparently in an attempt to make the show look better, which will inevitably be repugnant to Tolkien regardless.
Which is the reason I'm not watching it. I don't believe in watching a series that would deeply hurt and grieve the author had he lived to see its production.
[1] > Even after the merciless assault upon the Teleri and the rape of their ships, though she fought fiercely against Fĕanor in defence of her mother's kin, she did not turn back.
[2] > Galadriel was the greatest of the Noldor, except Fĕ'anor maybe, though she was wiser than he, and her wisdom increased with the long years. [...] From her earliest years she had a marvellous gift of insight into the minds of others, but judged them with mercy and understanding, and she withheld her goodwill from none save only Fĕanor.