In principle, I would dismiss every single time if a player accused me of racism. It's one of the worst and most damaging accusations that can be made IMO.
I'll give an example of how not to deal with it....
Cautioned a player (U13) for dissent, to which he replied "you're a joke, it's just racist this". I was dumbfounded, had no idea what to say or do.....so I asked the manager to sub him. Bottled out completely. In my defence, I was only seventeen at the time and I just didn't know what to do. Always regretted that one.