I don't want to derail this thread, but I don't know that we can right off label these things as sin. Advisable? Not really, but sin? It's a case by case study IMHO.
Dancing: I have two left feet and all the grace of a dancing bear, so it doesn't appeal to me. My wife feels the same way. I don't let my kids go to dances b/c of what it can lead to and b/c many denominational folks believe "preachers' kids don't dance." But is it sin to move in rhythm to clean music? Of course not.
When I was single I used to go to the dances our fire department would hold. Many saints did. But the music was clean, the lights were on or at least bright enough you could see and the idea was to listen to the music and a few folks might dance--most of the time it was older married couples enjoying a slow dance (one saintly couple were great dancers) or little kids acting silly to the amusement of everyone in the room.
Can I label that as sin? No more than I can a good friend and brother who is an avid square dancer or the elderly sister now passed on who used to come to school to teach us young kids old, old square dances. She was one of the soundest, most modest saints I've known who once publically refused to allow the song "When We All Get to Heaven" to be sung with unbelievers in a community play she directed saying in public, "Not everyone's going to Heaven."
I quit going to dances when a female friend of mine expressed shock that I would go to the silly fire department dances, saying, "Preachers don't dance." I don't know that I ever did again after that.
Cheerleading: A bit more difficult to defend. I used to love cheerleading as a kid, but not for wholesome reasons. However, in elementary school we allowed my daughter to be a cheerleader b/c it was a bit different. Were she in public school today would I? No way. It's a show that features the same moves you'd probably see in a strip joint. But in it's place, it could be OK.
Beauty pageants-Depends on what the element is. Swimsuits? No way. Immodest dress? No way. But for two years I have let my daughter participate in the local fair queen contest b/c with her status as an older adopted child b/c it boosts her self-esteem. She is not allowed to reveal her breasts nor wear anything sensual. In the right atmosphere, these can be all right IMHO.
Mixed bathing: This is a mixed bag. We were always taken to the park pool and I took our little projects children to the water park. I don't get in the water unless maybe it's at a motel pool with my daughters and that's rare. They aren't allowed indecent suits and sometimes I wear a shirt myself. Usually I don't see anything tempting as much as I saw things that made me wanna gag. But I don't fall out with folks on this one at all.
All in all, we have to take things on a case by case basis before labeling it sin. Some things simply have no profit, but they cannot be outright classed as sin for which we can withdraw from a person.
Note: If someone feels this needs to be the teachers' area, feel free to move it there. But too much work went into posting this! lol
