My partner and I are both African Americans. We've been traveling to DR- specifically Santo Domingo, but have been through much of the country- for years and have never felt any racial anything.
There are also quite a few African American expats in Dr (some are women), especially Santo Domingo. When we meet up with friends, whether Dominican or African American or Canadian or what have you, race is rarely if ever part of the conversation. That's because while moving throughout the country, be it guest houses, hotels, restaurants, car rentals, bars, clubs, supermarkets (I love La Sirena by the way), etc. race has never played a factor in what we do or how we're treated.
That being said, I have heard a story or two where African American women were mistreated (sexually harassed, cat calls and the like), with racist overtones. Overall though, we know quite a few sisters who come and go without a problem.
While there are racial issues in DR, I feel much more at home in DR than say, Boston. As a foreign traveler and especially as a tourist, DR for the most part is all about the benjamins in all their cartoonish hues. Your mileage may vary, but tell your friends the water's fine
CJ