NO! They should not!
I am still hanging onto my Labour Party membership by a thread and yesterday, Dawn Butler sent round an email blast encouraging women to apply for the Jo Cox programme before the deadline. I replied to it asking how it could possibly redress sex-based inequities in politics when it has already given awards to males and when current Labour councillors were supporting applications from spiteful boys like Lily Madigan. I explained that my current consideration was about cancelling my Labour Party membership, not applying for this scheme.
Hopefully, other women will have replied similarly.
By the way, Kristina Harrison, quoted in this article, is a lovely person who totally gets it - from a leftist perspective, no less! - and well worth following on Twitter at @KJ_Harrison. It can't be easy for a trans person to take this position in the current climate.