Saying that you are transgender when booking the appointment isn't actually saying anything about your sex organs at all. Imo, the terms 'transgender woman' and 'transgender man' are the wrong way around and confusing. If someone says "I am a woman" then it suggests they are biologically female, if they say "I am transgender" you would imagine that they have adopted gendered appearances and behaviour culturally associated with the opposite biological sex. So to avoid confusion Karen should have said "I am male, but transgendered", so that the beauticians could have made a judgement call about a male-bodied person who adopts cultural female gender norms. Although in the article it doesn't mention whether Karen referred to himself as a woman or a man, to say you are 'transgendered' it is possible you could be a biological female (but living 'as a man') so the staff could have reasonably expected vulva.
With regard to males in beauty salons as a rule, I find it really violating as a customer. Men sitting around or even hearing male voices when you are there for hair removal, etc it is so intrusive- such an affront - I never go back. Once I called to find out how much a leg wax was and a bloke answered the phone, asking me if I want a half-leg, full-leg, bikini wax or brazillian. I ended the call - I don't want to tell some random bloke I don't even know such personal information about me. Men should not be in these places - even male partners in the waiting rooms, etc. I remember once being in a place where there was a teenage girl sheepishly walking up to the counter and the receptionist saying to her 'so you are here for the full-body ipl'. There was a male partner of another customer that looked up with curiosity and clocked her - obviously processing this information about her (possibly something she felt hugely ashamed about and didn't want people to know) while she withered with embarrassment and had to take a seat next to him. Men should be polite enough to stay out.
This Karen pisses me off. I thought the whole thing about gender dysphoria is about feeling you have the wrong sex body. Brazillian waxing is about removing hair to get more of your fanny on show. If Karen genuinely felt dysphoria about his cock and balls, etc, I don't think he would want treatments to put them more on show.
I think it is some fuck-up fetishised 'right of passage' he thinks he needs to go through to join us ladies in the lady club and he didn't care how it would affect the staff or customers at the beauticians to draw them into his role-play against their will.