The term homeless people puts the emphasis on homeless, and allows NIMBYs to forget that these people are, in fact, people.
I really think this needs to be challenged. Sociologists need to prove this actually has some positive effect; I don't believe it does. Particularly in this case, homelessness was not an offensive term.
We just get ourselves into pointless debates about the politeness of a particular term, people looked down upon for "using an outdated term to talk about the issue" (and patting themselves on the back for "doing something for the issue"), while real people endure real suffering.
I don't believe anyone is going to suddenly see a person as a person because someone told them "we're relabeling that." If they're the dude in this article, they're going to roll their eyes and keep handing out fake money until people actually hold them accountable for their bad behavior.
This is not much different than the former University of Akron president trying to rebrand the university as "Ohio Polytechnic Institute" (to community outrage I might add).
The left wing of the US needs to stop relabeling shit and actually do something about it. Even at the local level, we have way too many mayors trying to solve homelessness by spending extra money to make urban design hostile to homeless people. That's not Republicans, that's not the labeling, that's a failure of the establishment to actually address affordable housing concerns and gaps in the social safety net.