Well, I'm not a WASP, but I am an American. Never a problem of any kind in 9 years of traveling there--that's about 10 trips and approximately 5 months on the ground in total, all over the country.

As a woman, I have been warned by Indians to not walk alone in the emptier parts of New Delhi (as opposed to Old Delhi) at night--but this has nothing to do with my nationality. I've also been warned to be careful in the state of Bihar and the far northeast of the country, but as it happens I've never had occasion to go to these places anyway so can't comment on them. None of this has to do with the fact that I'm American--there's just supposed to be more crime and political tension in those places.

As in every country, staying safe is mainly an issue of not acting like an idiot, and keeping your eyes open. If you're in a place where you feel uncomfortable, leave. That's worked for me in 20+ years of traveling to developing and developed countries.