In some of the most popular versions of Scarborough Fair, e.g., Simon and Garfunkel, it is the lady who is asked to do impossible things.
It always struck me as a strange song. At first listen, it sounds like a love song, but it mocks true love, traditional chivalry, etc.
I didn't know about the Disney version of Mambo # 5. Simple changes, but what a difference! OTOH, I think that making a really major change of meaning like that to a piece of music isn't altogether legit. Censoring a work doesn't fully remove it's original meaning.
I think that other no-nos would include things that relate to specific religions, faces, ethnic groups, countries, etc., in a negative way. Or maybe in too positive a way too, since that to some extant denigrates others by comparison. OTOH, that would kill songs like "Amazing Grace", Handel's Messiah, etc., which are quite religion-specific, but which are also quite beautiful.
How about Brain Salad Surgery? Most of is awful skating music, but I could imagine skating to one of fast paced "Karn Evil 9" sections, or maybe the opening number, Jerusalem (or the traditional music it was derived from). But some people could take offense, if they took the lyrics seriously, in a religious manner, in either case.
Another issue is that most teen age kids, even some pre-teens, are more knowledgeable about "adult topics" than some adults realize. Especially if they have access to the Internet, through a PC, iPad, SmartTV, or whatever, or they listen to the radio or TV - or play video games. (What values does Grand Theft Auto teach?) I think most younger kids know it's there - but it doesn't mean much to them, so they usually just ignore it. Give it a catchy toon, and to a large extent, that's all they hear.
If I wanted to avoid offending a judge, I would stay away from anything that had such a possibility. But that would kill a lot of traditional skating music, like Carmen, Bolero, etc. I think they are OK without the words. E.g., Mambo number 5 is a great tune.
But the tune to Scarborough Fair, like many traditional balads, is boring.
So my vote - keep the music, dump the words, and almost anything is fine.