The reason there are women's shelters exit at all is because a passionate group of women stepped up and put in the work to set them up, run the day-to-day operations, get legislation passed for funding and grants, put in the development work to get charitable donations, work with food pantries, clothing donors, grocery stores and a million other things you need to run a nonprofit.
I can only speak to my area, but if you're a man in an abusive relationship and escape and turn up on the door of one of the shelters that on paper only accepts women they're not gonna just kick you out in the cold.
The reason women's shelters exist is because activists in the 60's and 70's decided to build them and gain support, and eventually fought for funding. What is stopping any of you from actually building a movement to help homeless men, instead of complaining about the activists who try to help women in need of housing?
Why complain about the activists who focus on women's shelters because they're not ALSO tackling the issue of men's shelters, when you yourself could prioritize the issue of men's shelters?
Edit: The people who are dedicating their lives to helping homeless men do not see women's shelters as competition, they see women's shelters as valuable resources for knowledge with lots of carryover (such as approaches for addressing mental illness, drug addiction, and poverty). If you yourself have zero interest in putting in real effort towards a solution outside of opportunistic internet comments, why should anyone listen to you?
Take the lead, do some research, and build something.
Do you feel this way about institutions built for and by men, that women have demanded (rightfully so) access to, instead of building their own from the ground up?
Maybe ^^ is afraid of misandry and people like you who get angry/offensive when someone wants to help men as though it's a competition about who has it worse.
see: https://en.wikipedia.org/wiki/Women_are_wonderful_effect
not that setting up any shelter type would be easy of course but i vaguely remember Erin Pizzey (who set up the first women's shelter in the UK) saying in an interview that she tried at one point to get funding to set up a men's shelter but she couldn't get a single penny.
what she was taking about sounded like it was a long while ago but I seem to remember a guy in canada recently committing suicide because he had tried for years to get funding from the government for his mens shelter but same deal.
whether men have the same trouble setting up shelters in other countries I don't know
You are arguing in bad faith. You do not even need to argue.