The REU that I participated in was mostly white males. Out of about 15 students, two of us were females (both white), and three or so were non-white males, so well over half the students were white males. I was the oldest student in the program (early 30's), and there was another student (minority male) who was also older (about 25). I don't think that being a white male is going to keep you out of an REU.
I applied to the SETI REU for last summer and got rejected. Considering the nature of my current research, and the research I had started prior to the REU, I actually had a decent shot (I was almost surprised with that particular rejection). I applied to lots of REUs and got rejected from most of them. No big deal, as I also got offers from a few. And the one I ended up in, which resulted in research in a field that I was never exposed to, and that they don't do at SETI, and wasn't even what I thought I wanted to do (until I met with the professor and was so intrigued that I couldn't possibly imagine doing anything else at that point) ended up being so compelling and interesting that it has effectively redefined my future research goals.
I had two summers available to me for an REU, as an untraditional transfer student, returning from several years out of school. The first summer I had very few options for letter writers, as my writers barely knew who I was. I wasn't accepted into any program. The second summer I had started a research project at my school, and my professor from that project wrote my letters, as well as a professor who knew me well from frequent visits to his office hour. I got offers that year.
My suggestion is to apply to every program that looks interesting to you and has a deadline you can meet. Be open-minded about location, and accept that you might not get in anywhere, particularly since you're basically on new footing. If you have your heart set on SETI you might end up very disappointed. Nothing wrong with applying there, aggressively even (like contacting the professor you want to work with directly), but what is more important? Do you want to do research? Or are you so set on SETI that you won't apply anywhere else, hence not getting an REU at all? So by all means pursue SETI, but if it doesn't work out try not to get too disappointed, something else awesome will come your way.
Perhaps this summer you will get in somewhere else, in which case you might look more attractive to SETI next summer, between the research you'll be starting next semester, and wherever you might end up this summer.
On a semi-related note, I went to a professional meeting a few months ago (presenting a poster) and found myself sitting behind Drake at a session, and then hearing him talk, as well Tarter. Very cool