Not the same person but where I am there are shelters and community centers that offer these things for free. The facilities are not in as good condition as a gym membership though.
We have tons of shelters in the US too. Talk to any homeless person though and they’ll tell you they don’t use the shelter because it either: forces them to not use drugs, splits up a family, has lots of sexual assaults going on, or has more health related problems than it’s worth.
last time i took a shower at a homeless shelter:
you have to hand all your stuff to a guy at a window, he puts it in a bag, then you go to a medium sized room with several shower heads spraying towards the middle...
so you don't just get your shower, you get the water bouncing off a dozen naked homeless guys...
the water is a tepid, narrow, painful jet...
i caught scabies and athletes foot...
...
i've taken one other one at a shelter in another city and state and it was identical...
....
gym is way better, otherwise i'd rather take a bird bath in a random bathroom sink...
To add to @garbagebagel's point I am not sure that a homeless person with a car is very common in Eurasia.
But come to think of it, this depends on how much people are willing to move around and at what point are they considered homeless, e.g. if they can't afford to sleep anywhere except for the car but have a room in a next town etc.
Also, I am now not sure what is the statistics of ownership of things like cars in a group of homeless people in different places. Could be wrong about the idea that most homeless own close to nothing but don't know if such a statistic exists.
Not American. BasicFit and similar chains allow you access to all their gyms across Europe. Obviously, the car will be a problem here. If you can afford it, something like the citroen berlingo will do. They're everywhere, relatively affordable, and not super noticeable. If that's not an option, there's the library or public transport, combined with the occasional hostel. Not ideal, but better than sleeping on the street and not being able to wash at all.
A lot of those countries are just tax havens where companies like to "headquarter" their businesses and where rich people hide their money. Some have a low official population, and rely on exploiting foreign workers for much of the labor done (non-citizens don't count towards "capita").