Personally, I don't see the big problem. The Monk, as a class, is clearly inspired by the various kung-fu movies of the 70s, from the Shaw Brothers and certainly from the American TV series. I'm not sure how that makes it racist, personally. An individual player portraying a stereotype certainly would be, but no such player would be welcome at my table.
What I find interesting is the selective blinders folks apply to introducing something like the monk to a game like D&D. In a game where medieval technologies from across 5 or 6 centuries sit side-by-side and where a monotheistic setting is often changed to a pantheistic setting with little social change and where real, actual sentient non-human beings exist in huge numbers with no discernable effect on the social order....in this game, featuring characters like monks and barbarians sitting side-by-side with fighting-priests and wizards...well, I don't see it that far of a stretch, really.
I mean, D&D features a fantasy setting that is no more authentic than your average Renn Faire (and perhaps less so). Weapons and armor from distant and disparate real world nations sit side-by-side at the blacksmith, selling plate-mail on the shelf next to a rapier. Druids hang out with paladins and bards hang out with clerics.
I can understand if the monk breaks your personal suspension-of-disbelief...I just think it's funny where folks pick and choose which particular historical inaccuracy stands out for them, personally.
Me, I go with the MST3K theory, but to each his own. As long as you're having fun, then it's all good.