I live here and take BART all the time. My partner has some car crash trauma so unless I'm driving, she's using transit to get around and she generally feels safe. It can get sketchy at night on the weekdays but otherwise neither of us have had problems on BART.

FWIW people complain about sketchy people and odd comments on BART, but I've also been followed by a driver I merged in front of who circled the block, cut me off, tried to follow me home, then flashed a knife on me and threatened to shank me. Last year someone got mad at me on the freeway then brake checked me at an exit. As long as I use BART before 11 PM on weekdays I never really feel more unnsafe than I do when driving, but I also am not the type that likes to live away from people. I enjoy cities.