Its weird how many people dont get that a tolerant society should not tolerate intolerance. Yes, that is part of the concept.
Having that said, is this particular case even a matter of discrimination? From the looks of it, its rather simple: a service provider was asked to perform a service it doesnt provide (never), and therefore said service was refused. Which is fine.

What the person looks like, or in situations like the OP, what the genitals of the person are. Think of the bathroom situation people bring up. If a guy looks like a girl and goes into the womans bathroom and just does his business, no on bats and eye. If a guy that looks like a guy goes into the girls bathroom and does his business, people would freak out, or at the very least look at him weird, ask him questions, ect. Both the occupants and him would be annoyed/awkward in that situation. Vise-Versa. 

Do you guys remember the movie Step Brothers? Whenever I hear people constantly going on about what they are, always make me think of their dad going about how he wanted to be a t-rex.

I'm with Biology. Your DNA determines your sex. End of story. Anything beyond that is a mental disorder. Now it's a mental disorder that isn't a danger to anyone and nothing wrong with it, but its a disorder, IMO. Everything in your entire genetics/DNA point to you being a male or female and you believe otherwise. That is a mental disorder. End of story. If you were studying an animal, that is what determines it.

And what is it that makes a guy believe he is a girl? Does he just like doing girl things? Wearing girl clothes? Likes boys, ect. Who cares. Dress how you want, like who you want, do what you want, but nothing changes the fact you have XY chromosome and a penis between your legs. You are not a girl. They just want to be a girl cause all the things they like are associated with being a girl and thus they believe they must be or want to become one so that it fits their likes. They need to just accept who they are not care that boys shouldn't like dolls. 

so essentially there's no difference between men and women since as you say any distinguishing features between the two are just arbitrary?

in the case of this business would you rather the ownr have advertised her services for "menstruators" for example instead of women?

"I offer my services to biological woman only!"
I can see this happening

I personally prefer the differentiation of sex and gender as separate constructs as that seems like the most reasonable compromise. Having the two mean the same thing it difficult to separate the social and biological factors that comprise how we define individuals. If you perform all the social expectations of a woman then that is your gender though biologically you may have XY chromosomes and a penis. Once one goes through surgery it becomes a bit more difficult since that would almost require a third characterization to make life easier, I'll have to give that some consideration. 

Basically, I would argue that when one separates gender and sex in this way it is one's gender that is by far the most useful characterization on a day to day basis. Since we don't all walk around naked with our genetic tests printed on our shirts we use gendered social cues and secondary sexual characteristics to take a guess at sex without being certain. Realizing that one's gender and sex are correlated but one does not necessitate the other deals with the majority of issues surrounding gender/sex currently. In this way the salon would be a "vagina salon" rather than a "women's salon" and these kind of one-off issues would not come up. 

On whether or not being transgender is a mental disorder, if you dictate that anything that goes against one's biology is a mental disorder then I don't see how gay people wouldn't fall under that as well. Seems like an overly simplistic view of psychology based on "common sense" rather than doing the hard work of researching and studying the question. 

"I personally prefer the differentiation of sex and gender as separate constructs as that seems like the most reasonable compromise."

why? the two are correlated more than 99% of the time, in any other situation that would be far more than sufficient to establish a link between the two

" it is one's gender that is by far the most useful characterization on a day to day basis."

on a day to day business outside of activities related to biology your gender really doesn't matter though

does it matter if you are a man or woman when you pump your gas?

when you put your groceries in the kart?

when you climb the tree?

no not really it only starts to really matter when it comes to things like bathrooms or having balls waxed which are related to biology

"f you dictate that anything that goes against one's biology is a mental disorder then I don't see how gay people "

do gay people require surgery and treatment to fix a condition?

Sex and gender are strongly correlated, but that doesn't mean they are the same by definition. If there are situations where the two (social and biological gender/sex) are different then that gives the two words differing utility even if they would be the same 99% of the time. 

What comes up more, using gendered pronouns or dealing with a person's sex organs and/or genetics? If we lived in a post-gender world I would agree that sex comes up more, but in the current world I would argue gender is much more useful day to day for anyone not in the medical field. 

Are all mental disorders defined by things that require surgery? 

I have a friend that says that a transvestite without a dick is like an angel without wings.

"Sex and gender are strongly correlated"

so why are you arguing that they should be regarded as separate?

"If there are situations where the two (social and biological gender/sex) are different then that gives the two words differing utility even if they would be the same 99% of the time. "

can you give an example?

"What comes up more, using gendered pronouns or dealing with a person's sex organs and/or genetics?"

we use gendered pronouns in accordance with the sex someone appears to be, which comes out wrong like less than 1% of the time

"Are all mental disorders defined by things that require surgery? "

non sequitur, the point is that requiring surgery and lifetime medication for an ailment (being in the wrong body) in any other case would be considered an illness

why not in this situation?

Science isn't about sensibility, it is about being true or not.