This is an ineresting question. I didn't realize others did this, I have only seen this by another team once or twice. After each home game (win or lose) we line up and jog to the bleachers and thank the students that came out to the game by clapping. Being a boarding school we have very few parents attending our games. At away games we don't do it. I can't imagine the other team taking offense. It is not directed at them. And like I said, we do it win or lose. This gets into the 'politically correct' arena - and that stuff just annoys me. Needless to say, if this act bothers someone then they will be bothered. Our fans show their support for us at the field, I want to show the teams support for them at the field.
As far as shaking hands, I like it organized so that everyone gets to (has to) shake each others hand. The wandering around the field version allows some people to skip out on one of the sportmanship parts of the experience. As a youth coach I've had to deal with the spitting on their hand before the shake, or the 'psych' and downright refusal to shake hands, pieces. In HS the players are a little more mature, or they've been instructed what was appropriate. I believe if we allow the unsporting behavior to go on then we have missed an opportunity to coach. Now, is it sincere? At GSSM I'm guessing at least 50% (probably much higher) of the players are sincere with the shaking of the hands. I know I am. If it is not sincere, it should be. We give them the opportunity to grow, if they don't take it.........
Just my thoughts,