Personally I'd say that the needs of trans* women and cis women are often different, and sometimes conflicting or competing. No amount of wishing things were different will make them so, and resolving that conflict isn't going to be done by dismissing the arguments of any opposed women as irrational or transphobic.
I think that's probably true but, despite the fact that recent legal/social attitude changes are supposed to make us more tolerant of each other, there will still be rocky areas.
Thora made the point that she is a born woman and Rutita took her (gently) to task by saying that that implies an 'authority' over non born women. AuntiStella has only recently transitioned (if I remember these boards correctly) and has chosen to stay in her previous employment. She has said she has experienced difficulties but that is only to be expected because of her situation. She will not get everything all at once, she will get bits and pieces and gradually those pieces will combine and then everything will be nice. That's the way of life.
There's a nice philosophical line from 'The Second Sex' by Simone de Beauvoir (1973) which goes 'One is not born a woman, one becomes a woman'. We are all born babies and then gradually we acquire the outward trappings of our sex -the social stuff - and the social stuff brings with it certain statuses and lack of them.
Those who take strong positions are wrong, I think.
For a m/f transsexual (I mean someone on a life path to change their apparent sex as well as their gender - not anyone else on the spectrum) to expect perfection at the first step is unreasonable. Their whole presence will probably still be that of a man because they will still look and sound quite manly. As the years pass, the medication will take effect and things will become easier. For them, womanhood is not a trophy they can claim at the first step, it is a journey with no end.
For a woman to draw a line at 'born women' is also unreasonable. There are thousands of post-operative transsexuals in society that no-one knows about, even if they take their clothes off. They are women, indistinguishable from 'born women'. The special clinic at Charing Cross Hospital opened nearly 50 years ago and has been treating maybe 100, maybe 200 patients a year. That's possibly 10,000 from one hospital alone. Male teenagers who went there in the early days are now little old ladies collecting their pensions!
This is just a live-and-let-live argument.