It's a question of
Does equality = sameness?
Personally, I think no, not in the world we inhabit. E.g. I think that some positive discrimination legislation can be a really useful tool to try to bring about equality in unfair societies.
The trouble is, once you accept that to have equal opportunities and treatment, we have to have special rules in place for certain populations, it becomes very, very difficult indeed to figure out what those rules ought to be.
Going back to your DH's specific point about the Women's Equality Party, there has long been a problem about this. Should women as feminists be fighting alongside other marginalised groups, such as non-white people, LGBTQ people and so on, given that there are certain common goals? Or does that just dilute and blur the issues? I think the biggest problem feminism has had (apart from patriarchal misogyny, obvs) is that we are just such a heterogeneous group - so many different experiences, so many different issues depending on age, race, location, sexuality, income, education, culture etc etc etc etc
I think the trouble with having one Equality Party to represent all minority groups is that it would have too much bloody work to do.