Gay marriage affects nobody else - it simply affords a marginalised group of people equal civil rights. TWAW, if taken literally, impacts women's rights in numerous serious ways.
If the existing Equality Act exceptions to trans people's rights to access specified areas of single sex provision are removed - as Labour and Lib Dems are committed to achieving - and GRCs made very much easier to obtain, then any male person could declare that they were a woman, and access all women's spaces, whatever the women and/or the organisers thought or said. There would be no legal way to prevent this. This would include prisons, where almost all the women are survivors of male sexual violence, over half in childhood, and therefore find male people traumatising in what is, by design, a locked-in environment. It would mean a communal changing area, or steam bath, or women's shelter, or rape crisis centre. It would mean staff, and clientele, alike. It would mean that you had no right to specify that a female performed a smear test, or a mammogram, because a trans-identifying male person would meet your request to be seen by a woman clinician. It would mean that all provision for women, in all spheres, became open to any male person with a subjective, invisible, and unprovable claim to feel like a woman. All data would be captured accordingly. In effect, the category of women as adult human females would be lost, to be replaced by self-determined gender. It would erase us, in law, as a definable group. It would also ensure the erasure of women's success in most forms of competitive sport.
All of that directly affects us. It removes many of our own rights.
Right now, the pressure for the above is great. Lots of businesses are already being told that the Equality Act exceptions are almost never applicable. But they remain - and Labour and Lib Dems are committed, in line with Stonewall's lobbying, to remove them as discriminatory. If they weren't applicable, then that commitment would not have been made. We need clarity on those exceptions being both very much available to use, and lawful. And that women have a right to single sex-provision, should we, and a provider, wish for it. (It is not single-gender, though Labour weasel-worded with pretending that it was, in the last election.) Our protections, in law and in reality, rely upon recognising the difference between sex and gender.
Gay marriage has no impact on straight marriage at all. If you disagree on faith grounds, then fine. Nobody's asking you to be involved. Gay marriage affects nobody but the couple in question.
In fairness, gender transition itself doesn't, either. Clearly, people should have every right to express their gender, and their sense of who they are, in freedom and peace and safety, and anyone who is abusive, or discriminatory, or harmful should find the law against them. Gender is socially constructed, policing it is harmful to women as a class, but also to many men as individuals, and it's regressive and sexist to enforce gender stereotypes based on someone's sex. People should be free to dress, behave, and express themselves as they feel is most authentic to them. There's no issue with that. I absolutely support anyone in being able to express gender as they see fit. But gender is not sex. Sex cannot change. And sex matters.
Every human alive is so because of female reproductive labour - we are, in fact, the means of human production, and that is why we have been controlled. Access to and autonomy over women's bodies has been controlled by men, and still is, in many parts of the world. Being able to identify that, and ourselves, by sex, are absolutely essential. You can't defend women's rights, if what a woman is becomes nothing more than an idea in someone's individual mind. It collapses the whole principle altogether. At that point, even our consent to which males we allow to see us naked, or provide intimate care, evaporates. So does any way in which we can collect accurate data, or collectively organise as a class, in our own interests.
We are personally, directly, and immediately affected. The very category of what we are is erased. That's why I welcome the present government's assurance that our single sex rights, and the existing exceptions in law to even trans people with GRCs accessing sensitive spaces and provision, will be strengthened, and guidance to clarify that provided. It's not that I wish trans people anything but well. It's that I recognise the reality, impact and influence of biological sex on women's lives, and life chances. Gay rights don't impact straight people's lives in any way at all, and that's before you remember that women are disadvantaged as compared to men, while gay people are not advantaged compared to straight. The two are not comparable.
Jane Clare Jones has written a piece on this.