From what you write I think they are simply recommending clothing that will allow you to ventilate doing work outs, they don't want you to overheat. That is understandable.

If you really feel uncomfortable uncovered then perhaps you can reach a compromise? Maybe capri pants (or longer shorts) and T-shirt top might be a good half way between the two outfits?

I do understand feeling self conscious about your body but most people won't even notice the flaws you perceive about yourself.