Well, clearly the joke had an effect on the OP and made him/her miserable. More to the point, jokes like this have a chilling effect when it comes to reporting acts of egregious racism, because people are conditioned to overlooking "minor" incidents for fear of looking over-sensitive. People have been complaining about the PC police for so long that most people won't report offensive jokes in the workplace, even when they're in the right, because they don't want to make waves. And then, if something more serious happens, people are already in the habit of just ignoring racist actions because it's too difficult, too risky, to make waves.
Additionally, people who are in the habit of making racist or sexist etc jokes among themselves are eventually going to be overheard by patients, and that IS going to have an effect on patient care. Stuff that seems harmless when no one is going to overhear isn't actually harmless when, inevitably, someone DOES overhear a joke that was inappropriate anyway, but is REALLY inappropriate when heard by the "wrong" person.
Finally, I'd challenge you to think what the point of telling a racist joke is, anyway. We joke with our colleagues to form a bond of trust and rapport in the workplace, and to create solidarity. What does it say about us when our method of forming that rapport is by retelling racist jokes we learned in the second grade? Why are racist jokes so EASY to tell? Why do we find it funny to make fun of a stereotyped immigrant's accent?
I would argue that the function of the racist joke is to form solidarity by excluding people. We make fun of people who are different from us in order to feel we have even more in common with the people laughing at our jokes. If I'm making fun of a gunner jerk, I'm building healthy solidarity with pre-med friends by saying about myself (and indirectly, about my friends), "We find this behavior ridiculous, because we value teamwork and cooperation more than perfect grades at the expense of decent relationships." But if I'm making fun of a patient of a different race than I am, what am I saying to my colleague or fellow student, if not, "This person is different from us because they're Asian - and that fact alone makes them an acceptable butt of my humor."
TL;DR - racist jokes solidify racist hierarchies because they make insider/outsider differences clearer and discourage people from reporting racist actions or statements because "it was just a joke."