That actually sounds like a relatively simple one to resolve although the practicality might be a bit poor. The nonpolitical resolution is to use a space with 1 small unisex bathroom and insist that everyone keep it clean. If there isn't a consensus on who gets a special bathroom then there shouldn't be one.
So forcing everyone to change their meeting place to a venue with a unisex bathroom only is not political, but a trans woman using a woman’s bathroom is political?
Also, Helen still wants to be called Helen and still wants to be referred to as a she. By this logic, everyone must go by they/them? Or what?
> So forcing everyone to change their meeting place to a venue with a unisex bathroom only is not political, but a trans woman using a woman’s bathroom is political?
Nobody is calling for unisex bathrooms as far as I know, so it can't really be called a political choice. It is just practical - there isn't a consensus about who should get a special bathroom. How can there be a special bathroom if we don't know who is supposed to be using it?
> Also, Helen still wants to be called Helen and still wants to be referred to as a she. By this logic, everyone must go by they/them? Or what?
I don't see how to get away from that one, there is a fundamental rift between the people who think individuals control their identity and the people who think that identity is constructed by someone's peers (see also, shaking off an unwelcome nickname).
But that is an inescapable problem that has dogged humanity since before we were a species so good luck excluding it from any space. If it flares up and diplomacy can't smooth it out then some organiser is just going to have to make a call.
I think you’re missing my point here, which is that “no politics” is an impossible standard for any given social group even if the social group isn’t itself a political movement. There will need to be some measure of baseline politics, like trans people are welcome, jokes about Indian people being smelly are fine, gay people shouldn’t bring their partners around, “retarded” is/isn’t cool to use. Etc.