Whenever I get into a discussion about roles that can be played by any race, a couple of them surprise me. For instance, while you might not immediately think it, the role of Deloris in Sister Act can actually be played by any race, obviously including a white woman.
There is nothing in the licensing material that states that the role has to be played by a Black woman. In fact, when the movie was being developed, the role was originally offered to Bette Midler who ultimately passed on it. It was then offered to Whoopi Goldberg with one caveat, the script would be filmed as written. Meaning Goldberg didn't want anything having to do with her race in the film. Thus she is playing a woman who happens to be Black rather than having the film point out the fact that she is black.
So that answers the question of whether or not you can cast a White, Asian or Latina woman in the role, the answer is yes.
But just because you can do something, doesn't always mean that you should.
Just as is the case with shows like Hairspray, which shockingly you can do with an all-white cast, I personally wouldn't and would recommend you don't do it either.
While the role makes no mention of race whatsoever, I think not casting a black woman in the role, sends a terrible message to your community, especially if your theatre doesn't typically do diverse shows.
You also run the risk of confusing and angering your audience who bought tickets based on their knowledge and adoration of the source material, Broadway, and most professional productions which all have mostly starred black women in the role.
So in the end, yes, you can cast a white woman as the lead in Sister Act. But again, that doesn't mean you should. If you do, think really hard about what messages your sending about your theatre's value of diversity.