The point is that they, in fact, do accept everyone*. They then proceed to make them all the same by integrating them into the collective hive mind and replacing their unremarkabke biological attributes with cybernetic implants, true, but for the most part the borg take anyone.

^^*i know there is that Voyager episode where seven tells neelix how the borg did not assimilate the kazon, but in general they do take anyone, and assimilate them.^^