Holly Lawford-Smith's book* has stuff about liberal vs. radical feminism, and to me those sections gave an additional cue about one of the reasons for being inclusive of men who identify as women in feminism. The liberal feminism began with the desire to expand the rights and roles of the liberal political movement from just men to also women, so the starting point there was not in biological sex but in social and political exclusion of a group.
If you pay little attention to biological sex, then you wouldn't really care terribly much about new people wanting to enter the previously excluded group. Though of course women were excluded from the liberal rights on the basis of their sex and not because of some accidental oversight, and I don't really mean that today's feminists would think in those terms; just that the foundation of their ideology does de-emphasise the importance of sex in causing the subjugation of women.
My own impression is that progressive women trained in the universities from early noughts onward came into the feminist movement with a basic bundle of beliefs focused on intersectionality, privilege, and inclusiveness, and not on women's rights.
My own experiences from that era is also that very little critical assessment of that trinity (intersectionality, privilege, inclusiveness) at all, not even to point out when they can be misused (which they now are fairly often) was allowed.
The one radical feminist in one group who tried to do that, in fairly gentle and questioning terms, was kicked out. This was a signal others then accepted and either stayed silent or left.
When news reported about events where the basic bundle of values got thoroughly shaken (men ranked lower in race privilege raped women ranked higher in race privilege, say) it became impossible for that remaining group to address the nuances in the issues or to even speak for the victims. The Cologne mass sexual harassment, for instance, was then not even mentioned. The sexual slave markets of ISIS were never mentioned and so on.
And all this came from the privilege-based theory about ranking types of oppression and then only truly speaking for the ones who rank highest on some global scale.
Not sure if I could write that clearly enough, and of course it's only my own experiences from a handful of groups.
But I also think that lots of people of all kinds, including feminist, have just thought that the trans rights are exactly like the gay and Lesbian rights, without any infringement of the rights of others in most areas of life, and that the concept of 'rights' in the two cases is also exactly the same and equally fair.
*I recommend her discussion in that book about what feminism should or could mean, if it should be about trying to make women's lives in general better or if it should be limited to trying to make women's lives better where the reason those lives are not good has to do with being a woman.