the home school children do probably play sports unless there is some home school league too, they will get it then
you are making big assumptions that somehow home school children will be better adapted, less violent, less mean etc, not sure if that is correct.
I have a son in the public system, not is isn't the be all, and I wish he didn't just learn about first nations history in social studies but even if I taught him at home, he would still receive biased views of what was taught, except it would be my bias. He gets that anyway, so at least he might get a different view of the world in school. The more views and viewpoints to which you are exposed, the better.
The home school children join leagues, just like any other kid does. Believe it or not, if you want to play Little League in this country, or Minors, or even AAU Ball, you don't have to go to a school. If you want to play HS Ball, you still don't have to go to that HS. You simply have to be in that Schools district and you have to be able to make the team. Home Schooling really doesn't come into play there.
I don't know about you but in any sport I have ever been associated with, we have never had enough time to sit around and text crap or generally torment team mates. That's the thing about sports. If you are good or if you put out effort, team mates will accept you and yeah, you will get your normal amount of ribbing but it's not about social butterfly crap. It's about winning and that does not lend itself to bullying IMO. However, lets say you are correct and the kids do get bullied at practice. Do you think that they wouldn't also get bullied at school? If anything, all you are doing is limiting the exposure towards that sort of behavior.
Same with Football or Basketball or whatever.
I am making no assumptions. I am simply stating the fact that parents will generally love their children more then teachers will and because of this, they will not allow them to stray down the wrong paths as easily as will teachers or other students. No assumption there. I believe that's a generally accepted view.
My personal view on this is, if you teach your children right, raise them strong, it won't matter what other people do or say. They will not be strong enough to bring your child down. He or she will have the necessary background to overcome all that petty nonsense.