The same side which argues that it was wrong for a cake-making business to discriminate against a gay wedding is siding with a position which discriminates against transgenders. How ironic.
How convenient, though not unexpected, that you choose to ignore this:
It’s not even a trans issue. They just don’t wax penises no matter what your gender is.
Yeah, like arguments along the lines of of "We're not racist, we just don't put makeup on black skin no matter what your race is, we don't have training" and "We can't afford to install special toilet stalls and ramps for the disabled" are going to fly in racial discrimination and disability lawsuits.
When you are running a business and start making up excuses to reject people of protected classes then you will be forced out of business by the state with prejudice. The state will tell you that if you can't accommodate people of color, that if you can't afford to install the ramps and safety measures, and if you can't afford to train your staff on accommodation of people with disabilities, then you cannot operate. It is your obligation to accommodate people of protected classes for equivalent services.
Granted that transgenderism is not currently a protected class and that it is currently legal to discriminate against them. But if you believe in transgender equality, and believe that transgenderism should be protected like race and disability are in many states and countries, you should likewise believe that they should have the right to the same services irrespective of their special needs.