I have 3 boys and it doesn't mean I only have to deal with 'half the shit'.
What me and my DH deal with, is bringing our boys up to respect themselves and everyone around them, regardless of their sex/gender.
To try and teach them not to bow to peer pressure and to remember that every single photo they send digitally (whether rude or not), means that they completely lose ownership of it.
We also try to teach them not to judge or join in with the gawping/ridicule of anyone who does make a wrong judgement call, meaning their photos (whether rude or not) get passed about against their will.
I was proud or my (then) 14yr old when he went to his head of year and told her that both boys and girls were passing round a topless photo, of someone in their year group.
I was even prouder of him when he sat up half the night comforting her on Skype, telling her that just because she made a wrong judgement call, it doesn't mean her life is over and that she's not a decent person. She eventually realised this and with the help of her other friends, she managed to get over massive embarrassment/ridicule.
I was just as proud when he spent hours talking to his friend who got beaten up in town, the assault videoed and passed around Facebook and Youtube for all to see.
So actually, the fact I have 3 boys and no girls means fuck all when you put it into context. I really don't envy being a kid/teenager today. At least I didn't have to worry about mistakes/embarrassment going viral.