M.R.
I am a high school health and physical education teacher and while 'activity classes' are not my primary focus, I do teach at least one class each year.
Some teachers have gotten really good at making the 'team selection' process fair, equitable, and dignified. Some teachers are still stuck in the dark ages and let the athletes be the captains and then pick their teammates (in my opinion, that's just awful).
Some ways that I do teams:
"reverse picking" - I pick four kids at random to be captain and have them sit at the front of the gym. Then, I pick 4 kids at a time to go sit behind a captain of their choice but they must all be on different teams (i.e. no two kids in a group of 4 that I send up can be on the same team). I go through this process until every kid 'chooses' his or her team.
partner flashcards - I'll create a list of like celebrity names write the first name on a card and the last name on another card. I shuffle the cards and then pass them out at the beginning of class. Their job is to go find their partner, so like if you got the name 'Britney' and I got the name 'Spears' then we'd be partners for the day or the unit. I have never had a problem with kids trading their cards.
team flashcards - same as above, but I'll have a theme where they have to go find their team. For example, with foods I might have 6 cards of fruits, 6 cards of vegetables, 6 cards of meats, 6 cards of beverages, etc. and when I say "go" they have to try to figure out their theme and get with their team.
the blind draft - I usually do this at the end of a unit and let the team that won become captains for the next unit as a reward (since I use fair methods, the "winning team" isn't one that is usually "stacked"). The captains get a print out of the class roster and sit apart from the class. Everyone takes their turn picking someone and they have to alternate boy then girl. There is NO talking other than saying the name of the person they want. They turn their completed rosters in to me and then I type the rosters, putting the names of the kids in alphabetical order so no one knows when they were picked.
The emotional safety and well-being of every student should be the primary focus in EVERY class (not just gym) because kids who do not feel safe, accepted, and comfortable in school may not be able to succeed to the best of his or her ability...and as a teacher, isn't it my job to try and make sure kids do just that?