You are now entering Disney. Please set your watches back to 1958.
It's that level of thinking - old-fashioned values or as close as they can get to them. They don't want the place cluttered up with sk8ers and Goths and the like, upsetting Middle America.
As regards thinks such as tie-tops, halter necks and so forth, it's not only Disney. It might be perfectly legal and normal for women to sunbathe topless on a Spanish or Italian beach, but before they leave said beach, everyone must put on street clothes -beachwear stays on the beach.
There's also the careful middle-classness of it all. Respectability, neatness, conformity, all equated with comfort. Disney parks are respectable places for respectable people with polite, well-behaved children.
I mean, I don't know what the ride was, or what the top was like in that specific case. What I do know is that, when my daughter was 16 or so, her year group were taken on a post-GCSE school outing to a local amusement park. An 'acquaintance' (ie mortal enemy) of Jens', who is a rather well-endowed young woman, made an unfortunate fashion choice, then compounded it by going on a ride that turned you upside down, high in the air, for some time. There was, shall we say, an incidence of 'double fall-out' which drew every adolescent male in the park to that ride for a while. Needless to say, Jen was highly amused by the whole thing!
This being the UK, the park staff were fairly robust in their response to the girls' complaints: "You knew what the ride was, what it did. If you chose to go on it dressed like that, it's your own look-out!" In the US, I suspect that park staff are expected to be more vigilant, as Americans seem to be more strait-laced than we Brits. If there was a possibility that the ride might have dislodged an insecurely-tied stringed top, I would understand the operators' caution.