My parents were and are totally okay with me playing all kinds of games. In fact, I myself limit what games I play. I have never played Gears of War, the Doom series, or any of the GTA games before San Andreas because I thought that they were over doing the gore and vices.
In the case of Doom (especially 3) it was too scary. I hate being scared, and I am scared easily, so that's why.
The only thing my mom was ever worried about was in battlefield vietnam (one of the first games I played multiplayer). She didn't want me playing on the vietnamese team because she was iffy about shooting american soldiers.