Fine, I'd agree with that with the proviso that none of this means we have to agree that trans women are women or accept them in women only spaces.
Being trans in itself isn't illegitimate, threatening or wrong. Describing yourself as something you are not (i.e. a woman if you are male) or entering spaces intended for the exclusive use of the opposite sex, very much is.
See the difference?
As for "appropriate healthcare", I believe trans people should have equal access to healthcare compared to the rest of the population. I'm not sure that puberty blockers, cross sex hormones or extreme bodily modifications are really "appropriate healthcare" though.