It really depends on the type of chapter you want to join. If you're looking to join the larger, traditional, more "fratty" chapters then yes- wearing Abercrombie/Aeropostale will hurt your chances but you should be fine with Polo and Lacoste. As long as you aren't wearing anything from their more trendy lines (stay away from big graphics like
this)
I would stick to conservative clothing at UF. Khaki shorts or slacks (depending on the event), solid color polos, button-ups, etc.
Being Asian might put you at a disadvantage depending on the chapter.
Just act natural and let the conversation flow. If you try too hard, it'll be obvious.
ETA: No cargo shorts!!