We saw them stop a lady at the turnstiles who was wearing bikini top with no shirt. Saw here later in the day with a shirt on. I believe they require you to have a shirt on outside of the water parks.
I think a rash guard top with board shorts would be ok. Rash guards look enough like normal tops. But I can't imagine it would be comfortable to walk around in for long.
The ponchos are awkward but they do help. If you want to avoid them, wear clothes that dry quickly. I think that trying to find bathing suits that look like clothes will not work.
We brought rain jackets last month. Yes, it was warm in June, but they weren't nearly as bad as ponchos. Mine and DH were Columbia, the boys wore some that I bought at Walmart for less than $10 each.
I think a rash guard top with board shorts would be ok. Rash guards look enough like normal tops. But I can't imagine it would be comfortable to walk around in for long.
DH and DS have chimed in on this before with big huge "ouch" expressions on their faces. The mesh "underwear" in trunks/board shorts isn't something most want to wear to walk around in.