Borrowing Occam's Razor, I think it's much more likely that she's referring to the old, persistent question of men participating in (and more critically at the moment, attempting to lead or define or speak on behalf of) feminism. The role of men in the movement(s) is not really much of an everyday issue or question for most feminists, but very often comes up from people curious or learning about feminism and/or wanting to criticise it without fully understanding it.
In radical feminist circles, it goes without saying that men cannot be feminists, although they can certainly be "allies", understand feminist analysis, study feminist theory, actively support some feminist goals, join with feminist groups in common cause.
Among Marxist, materialist, socialist feminists - I'd assume KIS falls somewhere in this group if she wanted to join UK Labour - there's more of a split with some feeling that the basic issue is class and all people should work together to overthrow the system and deal with sexism "after", and others feeling that class is largely overdetermined by other factors and sex is a critical one and so many feminists should focus on the larger issues through that particular lens.
Liberal feminists tend to see the class of men as a benchmark of where women should aspire to be, and can be all over the map on inclusion of men in feminism. What no feminist will do, though, is centre men in feminism at the expense of women in a political-economic-social-cultural system that structurally and systemically marginalises and exploits women and girls on the basis of sex. This has nothing to do with "hating" individual men or men as a class, it's just logic.
I'm not very familiar with KIS apart from knowing that some of her work is used in the HoC, so thanks for linking to her site. I'm actually surprised there's so much on there catering to men and male views (and/or perhaps to women who support her but feel the need to justify her work and views to individual men in their lives). Likely, also, she's received a lot of blowback on why she's centering women, so perhaps she's chosen to put it out there in writing rather than constantly explaining herself. She seems to have a pretty positive view of individual men and men as a class; why else would she take the time and space to write and showcase so much addressed TO men, almost all of it constructive?
Probably she IS a good fit for UK Labour - while she might not pass the (counterproductive at the moment) vetting process to become a Labour candidate, they'd likely do very well to listen critically to what she's saying.