Can we raise godly kids in this culture?

Feel like I'm fighting an uphill battle every single day. Turn on the TV, check the phone, go to school and my kids are getting bombarded with stuff that goes against everything we're trying to teach them. My wife thinks I'm being paranoid but I see where this is headed. Do other dads feel this way or am I just being overprotective? How do you balance protecting them from the world without making them sheltered?