Whilst I agree that we should unite, in practice this is very difficult - and that is because women (and men) pull in different directions and there is no clear path forward for what feminism should be and how it should look. Take for example sex-work, some feminists consider it empowering, if a woman wishes to work as a sex-worker then she should be both allowed and entitled to do so. Other feminists see this as a market which springs out of women as property. Which is the correct answer to unite behind?
And yes, I agree. Trans-women are women, but that doesn't mean it is a completely problem free statement or that it doesn't throw up complicated issues that aren't easily resolved. I wrote an article today about such a thing. https://medium.com/lucid-nightmare/bearded-male-powerlifter-smashes-womens-record-by-100lbs-4fc3530dbde2
And yes, gender-egalitarianism is my preferred way of seeing the world - because feminism often appeals too heavily to misandry, which gets to sneak under the gate. Sometimes fairly, sometimes unfairly. Gender-egalitarianism doesn't talk about mens rights or women's rights, it just talks about rights.
With sex-work as an example, the two competing feminist views lead us to.... both men and women are allowed to commodify their body if that is what they wish to do. Liberal societies permit this and there should be no judgment attached. However, such commodification needs to be fully understood, licensed and legal to prevent abuses of power. There should be safeguards in place - along with a robust tax system. Given this licensing and tax implications there may be less of a take up for sex work. That is gender-egalitarian. :o)