The problem with this question is that it varies wildly by both region and specialty. I know MDs in PM&R that love DOs, are outnumbered by them, and wish they could use OMM. In states with huge DO populations, you usually don't see much bias. Go out to states with a really low DO to MD ratios and that could change, like having places explicitly say that they won't take DOs.
Wherever you are, I doubt you'd have an issue finding a job. Also, as cliquesh mentioned, don't go just by the ad. You won't know for sure whether they really mean "no DOs" or whether they mean "physicians only". Some job descriptions do explicitly say things like such and such board certification required, where its only the allo board, but again it could just be an issue of them not expecting to get apps from DOs, not of them not wanting apps from DOs.
It was a blanket statement that ostensibly called white male MD's racist AND sexist at the same time. You know it, I know it.
Besides that, his statement isn't based on his real life experience, unless he's served on a hiring committee in his illustrious pre-medical career; we know that he isn't a physician that's applied for jobs. Case in point, what statements like that do is contribute to a tolerance of labeling professionally successful white males (as racist and sexist) socially acceptable, and that's not okay.
Wow did you jump to conclusions quickly.
He never said white. Granted he said male, and granted he said MD, but he never said white. Heck he didn't even say non-white, tan, brown, black, yellow, orange, green or any color, he said "different skin color." Read it again. You could very well assume he was referring to any group of male doctors of one race/skin color (black, white, brown, etc.).
Also, last I checked, MDs didn't encompass all professionally successful individuals.
Discrimination exists. His statement pretty clearly implied that discrimination exists, so DOs may experience bias, but its probably the same level of bias that anyone would experience when approaching a job in a small practice with a predominant race, gender, degree, and to add to it, age, city of origin, sexual orientation, hair style, football team, fashion sense, and any other random thing that people can discriminate based on.