Mulan was not a geisha. Equating a Chinese woman with a Japanese geisha is insulting in the sense that it appears that all Asians are the same to the person in a Chinese costume with geisha makeup, rather than understanding about having distinct cultures.
While I am not all that familiar with Mulan and the movie, etc... This is probably true.
However, even that would have absolutely no bearing on whether my child would be a white-face (geisha) Mulan.
I am not all about the over-the-top political and cultural correctness.
It is to the point of being ridiculous.
My reasoning for my opinion and advice that I would not want to have my young child in geisha white-face is all about other issues.
Some of which have been mentioned here (young child going thru a day at school in that much make-up, etc...)
And others which have not been stated that directly... (the idea of a young girl portraying a geisha)
If I wanted to be a Geisha for halloween, or buy a quilt that I personally find beautiful/attractive... I really don't care that much about the so called politiical/cultural correctness. And, I will admit that.
But, hey, that is just my opinion... (I have a much bigger problem with those who think they have the obligation and right to express/enforce a negative opinion and expect somebody else to never, ever, do anything that one just might find offensive. As the OP described.)
In the end, it is just a Halloween Costume.
How many other Costumes are we going to hear about this year that are not 'sensitive' or 'politically correct', and therefore, some person might just happen to think is 'offensive'. It is beyond ridiculous any more.