i don't think that either of the reactions are wrong, per se, although i don't think it's reasonable to use language about "safety" or language about transphobia, unless the language about transphobia is directed at language about "safety", in which case it's true.
it's a comfort issue. frankly, i wouldn't want to go to a women's spa and end up around people with penises, either. that said, that's my own comfort level. i mean, we're talking about full nudity, here.
here's how this ought to work: it ought to be up to the community that frequents the facility to decide what they feel comfortable within. unfortunately, we don't live in a society that upholds co-operative ideas, so it has to fall upon the business owner to make decisions regarding what she wants to allow in her business, and up to clients to vote with their feet. she may want to consider surveying her customers, of course. but, if another spa opens up across the street with a more liberal access policy, and it attracts a lot of business, then the people have spoken regarding their comfort level; if that business fails, they will have as well.
i would suspect that the business with the stricter definition will be more successful due to the nature of the service, and i don't hold that truth against anybody. trans people have an obligation to respect certain boundaries. she should back off on this.
further, this is access to a spa. it's just about the definition of non-essential. and, i do not believe that a court in canada would argue it has jurisdiction to interfere.
if this upsets you, you have the right to start your own spa with different rules, but i don't think you have the right to tell this business owner how to run hers.
http://www.cbc.ca/news/canada/toronto/body-blitz-transgender-policy-1.4158397