You can always try passing the phone to someone else...
There is really nothing racist about it...a black dialect, especially southern, is very distinct. But white people tend to do that too. It's all over, and mostly in those with an education level below standard. I've noticed that some people, especially black people (I, along with several of my black co-workers, HATE the term African-American. You born in America? You're AMERICAN!), tend to speak too fast and that's why they don't bother with the consonants. It's a lazy speech thing that people in a region tend to unconsciously duplicate, if they're not careful. I have to ask people to simply slow down a little, and sometimes that works.
I'm not sure what the protocol is for a relay operator, but perhaps you can simply begin by saying "You need to be sure and speak every word clearly so that I can understand and get everything correct, OK?" Sometimes this helps with the speed, too, as people slow down to be more articulate. (they tend to speak softer, too, but I digress...) If they start talking too fast, just ask them to slow down a bit. They only might take offense if you say "You're talking too fast." Say something like "Woah, can you say that again, a little slower? I'm from..." and pick a region of the country that sounds like it's in the opposite direction of the caller. Calling yourself a Yankee will surely elicit some amusement...but I'm sure they'll comply.
If not, there's not much else you can do. Heh...I'd like to see someone relay from a true cajun who, while managing to get their intent across, absolutely mangles the sentence structure and pronounces some words with a inflective flair! Dey not too diff'rent, dem, fom somma dem people, dere, who came from dey country ovah dair! LOL! In other words, they're not too different from immigrants who learn english as a second language. I was born in New Orleans, so I've heard it all!