sylvanian did you just reply with "well duh"? Very smart... I have no idea how to answer that well thought out response. I'm humbled...
However, the parallels between oppression (and scare mongering) of gay men and women, the battles they went through to be recognised legally, and fighting against the public and government which deemed homosexuality as curable and a mental health issue, are clearly obvious. As per the remarks on this post and many others on the Feminism board.
In 10/20 years time, transgenderism will be as widely accepted as homosexuality.
underhereye also has it spot on when mentioning the respect issues regarding transwomen respecting a CIS woman's right to privacy and a safe place for us.
Personally, I have less of an issue with a trans woman using the same changing rooms or loo. I have more of an issue with communal changing rooms, toilets, hospital wards etc...