Either way, homeless people making homes on transit isn't a transportation issue, it's a law enforcement/social services issue.
The people who seem to complain about it most are also the sort of people who won't ride transit anyway and just use it as an excuse to stay in their cars.
Getting rid of homeless/ppor people overnight wouldn't fix the perception issue immediately. It would take a while for word to get out that the buses weren't associated with being poor again.
Strangely, I think that making transit completely free removes some of the "poor" stigma. If two things cost money, then you compare the prices and benefits of both to decide what to pick. If one option is completely free, then that comparison isn't performed the same way because of weird mechanisms in our brains. Most middle class people will pay more to drink name brand Coca-Cola instead of an off-brand cola, but if you made the off-brand cola free, then a lot of middle class people would start drinking the off-brand stuff. It's not really rational, but middle class people love a bargain. And once the middle class people start to realize how much of a bargain they get from free transit, then more will start riding and the proportion of poor people will go down, and then even more middle class people will start using it.
Directionally, I think it's reasonable to assume that bad smells negatively impact ridership. It seems all we disagree about is the magnitude. Given how few people ride transit now, even a small number of folks who avoid transit due to smell seems likely to be a decent sized percentage of overall ridership.
I'd bet that ridership would go up 10+% if you could magically remove any hygiene and perceived threat issues. Although now we're well into the territory where we are each just projecting our own opinions, because AFAICT neither of us have data to back our assertions.
Buses do need to be cleaned regularly. When that doesn't happen, the homeless might be blamed, but a more fair target might be poor administration.
/s
I'm not implying anything about homeless people other than IME they don't have the hygiene of a housed person. And if you read the scope of my comment, I was specifically addressing their strategy suggestion of increasing usage.