The first thing is that a right to a peaceful, authentic existence does not necessitate distressing and excluding females. That isn't peaceful or authentic, it's male supremacism.
The second thing is that female people have a right to a peaceful and authentic existence too, equal to the consideration given to TQ+ identified male people.
This cannot be done by forcing male people into female spaces and saying this is lovely, progressive and peacefully authentic, because it obviously doesn't work and it never will work.
Third spaces would work. Mutual respect. Mutual tolerance. All needs equally met and respected. That kind of thing.
The third thing is that an existential crisis if someone will not do what you demand to their disadvantage, does not mean the other person should just give into you. It means the person needs help with coping better with boundaries and their emotions.