Jeremy Corbyn and Zarah Sultana’s new party is already split over its policy on transgender issues.
Adnan Hussain, who will become one of the group’s six MPs, said last week that trans women are “not biologically women”.
But Ms Sultana declared she would “always” speak in support of the rights of trans people and insisted “bigotry has no place” in the new party.
The MP for Blackburn wrote on X: “Women’s rights and safe spaces should not be encroached upon. Safe third spaces should be an alternative option.”
Fewer than three hours after Mr Hussain’s post, Ms Sultana said: “I’ve always stood with the trans community, and I always will.
Mr Corbyn has previously spoken in support of trans rights, putting him and Ms Sultana at odds with Mr Hussain on the issue.
On being accused of “trans hate” by India Willoughby, a transgender journalist, Mr Hussain said: “There was no hatred expressed, India, it’s a conversation that needs to be had.
“Agreeing with women on their need for spaces exclusive to them is not an expression of hatred to any other community. I stated the need for safe spaces for trans people, that’s not hatred.”