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Fiddler does have racial musts...Ummm... I won't go into that Good thing, because it would say more about you than the show. I've seen it performed a half dozen times, by everytihng from a polished Broadway cast to a mixed-race high school in Georgia, and the show supercedes any bias you might want to throw at it.
MATTRESS is an excellent choice, but 42ND STREET and CRAZY FOR YOU (and ANYTHING GOES, for that matter) are dependent on a chorus that can tap dance, which is pretty much becoming a lost art form.
WHISTLE has its own racial issues (See the first act finale, and I doubt you could rewrite the lyrics to suit).
The R&H warhorses -- CAROUSEL, OKLAHOMA, and SOUTH PACIFIC -- are all good choices, although PACIFIC needs a huge male chorus to work.
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