Any prejudice against someone is not nice - however this is not a prejudice...
Men in male spaces
Women in female spaces
not tricky to understand - so does that prejudice anyone - no, everyone is born either male or female, -> has access to a space, so there is no discrimination.
There is no logical reason why someone who is a 'transwoman' needs to go into a female space - their only excuse they could offer would be that they don't feel 'safe' in the men's space - how deeply ironic and insensitive - because that is exactly why they should not be in a female space as they are a man in a female space.
no idea what is meant by 'cis-men' - there is no such thing - you are either man or woman / male or female - there is nothing else, that is biology / science / immutable.
So to put it correctly - if a man goes into a female space...
ahhh - well that is exactly the discussion, because someone who identifies as a trans woman is a man.
It doesn't matter how you dress it up / what words you use / how you wish to define or identify yourself - a man is a man and a woman is a woman - it really doesn't get more basic than that... pretending that some men are women and therefore are allowed into female spaces is a lie designed simply to give those creepy people access to a space where they should not be, and the only reasons are nefarious.
and equally, sorry, but you are not welcome in the men's spaces - if I am in the men's loos and a woman comes in - that puts me at risk of accusations etc. - the men's loos are for men. If there is a queue then the answer is a better ratio of loos for men / women, not people using the wrong loos.
and you might wish to understand the true meaning of transphobia - phobia means to be scared of something... ;)