There have been loads of cases of transwomen trying to force their way into female safe spaces. The rape crisis one in Canada was actually in my mind when I wrote the above post. There have been numerous cases in prisons too - notably with men who are in prison for raping/murdering/assaulting women, demanding GRS and hormones be provided by the state and then demanding that they be housed in female prisons. There have also been cases of transwomen with penises intact using female showers and changing areas at sports venues.
Transwomen also managed to get Conway Hall to refuse to be a venue for the RadFem 2012 conference because they protested that the conference and its speakers were transphobic because they do not accept that transwomen are female and therefore they were not welcome at this women only conference.
So yes, there are transwomen who want to get into women's spaces. For lots of transwomen it is about validation, about 'passing', about having biological females accept them as being the same as biological females. Ironically this behavior is so full to bursting of male entitlement and misogyny that it clearly marks such transwomen out as being nothing like biological females. And it smacks of delusion/narcissism/mental health issues.
And due to the Gender Recognition Act, these transwomen have the law behind them. The law agrees with the fantasy that a man who wants to be a woman is the same as a biological female.
I have often in these sorts of discussions been told that such behavior is very rare and in no way representative of transgenderism. But that isn't true. Not only is the behavior not that rare, but in addition there is a pattern to it. And in addition to that, when there is case (like the rape crisis one for example), hundreds of transpeople and liberal/progessives will mount an internet campaign in support of the transperson and attacking those who will not defer to them.
If you want to get a feel for what goes on, start a trans critical blog or tweet on trans politics in a critical way. You will be flooded with threatening, abusive, misogynistic communication - if you are anonymous attempts will be made to out you and make your identity public, you will receive death threats, rape threats and be told that you are driving transpeople to suicide. You will notice a pattern in the behavior, language, etc which will remind you of what commonly gets called narcissistic rage.
I sometimes wonder if it is the hormones - if giving female hormones to males does something to mental health. Having said that, plenty of trans extremists don't actually take hormones and they still exhibit this aggression and delusion.
Of course one must assume that there are also lots of lovely reasonable transwomen who just want to get on with their lives, accept that they are not the same as biological females and have no desire to muscle in on women's spaces, politics and rights. Indeed such a group are trying to organise and speak out - they call themsleves New Narratives