In a hypothetical society where everyone is equally wealthy, no one would be forced to leave their home due to rising rents.
In a hypothetical society where everyone is equally wealthy except for a small number of billionaires, then at most a small number of people etc.
In our current society with a great disparity of wealth levels, etc.
It isn’t a 100% positional good.
You can actually build more housing units, if you’re allowed to.
Not uncoincidentally, this would also lower housing costs and the risk of gentrification in the first place, or at least lower damage associated with it.
Or we could just continue not building new housing units and simultaneously say white people leaving an area bad and also that white people moving into an area is bad. Surely this will help the poor, somehow.