It seems logical to me that radical feminism and more conservative with a small or even a larger C will be aligned on this point.
I don’t know RL and I have not yet read the piece, but I do find myself reading the Times now, which is conservative with a small c, surely, yet has some of the best coverage on this issue.
Conservative or even centre people believe that men and women are different because it upholds the social structures we have today. Men are the main breadwinners, women are the home-makers. Sex gives rise to sex roles.
Radical (second wave) feminism agrees that sex gives rise to sex roles, but called them gender roles to distinguish, and sees them as oppressive, not the foundation of social order. However, radical feminism also believes that men and women are different (biologically, based on sex)
The argument against the TRAs hinges on that fundamental point. Both conservatives and radical feminists argue that men and women are different based on sex, not an idea of gender in your head. They differ about the implications of this.
So it is equally possible that fundamental evangelicals will agree with radical feminists that men cannot be women and there is sexual difference, but the two groups will differ about the implications of this.
None of the above groups base their arguments in double think. The libertarian left (is there such a thing?) argue that men can be women, defined through gender stereotypes, whilst suggesting this is progressive. The radical feminist position is going to end up seen as right-wing because it harks back to ideas related to sexual difference which women sought to dismantle, and which are now seen as regressive - however, no women’s movement ever argued that sexual difference does not exist.
I am tired so not making much sense.