Interesting. Now that I think of it all the women I know who get waxed have at one time or another commented on girl talk with their....whatever the hell the folks doing the waxing are called. And the girl talk almost always involves dudes who come in for the deed. So while I have an admittedly small and second hand sample size, it would seem more the exception than the rule that they'd refuse to wax based on ones tender bits.
All that aside though, the person doing the waxing clearly has the right to decide whose junk they touch. And if she has a clear and across the board no touchie penis policy, that's well within her rights. The service wasn't denied because the person was trans, it was denied because she doesn't touch the general publics dick.
Sounds more, like usual, a radical looking to make a spectical of themselves. Book an appointment with someone else who is fine waxing your OEM parts and move on with life. There's plenty of them.
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