If you reclaim a parking space for another use (such as building accommodation for families or an animal shelter), you're not depriving the car of anything, it's an expensive, large piece of metal and is not sentient.
Next, you'll say that you're depriving car owners from the practicality of parking their vehicles anywhere they like. I'm perfectly fine with depriving car owners from this convenience to allow a human being to have a roof over their head. (speaking from direct experience as I've just minutes ago had to park my car 1km away from home because the city is currently building housing and has restricted parking space nearby)
Then, some might argue that one should be ashamed of helping animals while humans are suffering. That's the exact same train of thought with «we can't allow more migrants in, we have to take care of our "own" homeless people».
This is a false dichotomy. Western societies inequalities are growing larger and larger. Me trying to do my part is insignificant. Me donating to human or animal causes is a small dent into the mountains of inequalities we live on top of. Us collectively, we do make a difference, by donating, voting and generally keeping our eyes open about the world we live in...
Finally, an entirely anecdotal pov: I've witnessed several times extremely poor people going out of their ways to show solidarity to animals or humans. I've also witnessed an awful lot of extremely wealthy individuals complaining about the poor inconveniencing them by just being there, whose wealth was a direct consequences of their ancestors exploiting whose very same poor people.