Both movements are products of an attitude that people need to be protected from anything dangerous or risky. That way of thinking drives me crazy.
I wrote about a similar issue a few years ago, and I included a long lost of injury statistics. I'm not going to do that this time, because the numbers are 100% beside the point.
Football is dangerous. Boxing is dangerous. That being said, not everything dangerous should be illegal. People have a right to chose what to do with their bodies. If people don't approve of full contact sports, THEY DON'T HAVE TO WATCH IT!
It's the same mindset as wanting to ban smoking in bars because some people don't approve of it. If someone doesn't approve of smoking, THEY SHOULDN'T GO TO BARS! Smoking may be dirt stupid, but people should have the right to do it. Of course, if they smoke for 30 years, they shouldn't be able to sue tobacco companies. Part of making choices is accepting the consequences.
Likewise, people have a right to participate in full contact sports. However, if they do, they shouldn't be able to sue the league when they get a concussion. Full contact sports involve FULL CONTACT! You play the game, you take your chances. But, that doesn't mean we should water down the game.
We can build safe cars, recall dangerous baby cribs, and do 1,000 other things to protect each other. Yet, we'll never be able to make life 100% safe. We shouldn't try. People need to be free to be people, not robots.
A wise man once said, "Sitting in church, eating bran flakes is safe. You take your chances with everything else."