When I first moved to the Bay Area, San Francisco was described by one person to me as "quite conservative actually." At the time, that seemed unlikely. However after a while, I can now see why this is the case.
I am not 100% sure that your implication really tracks with conservative behaviors. I would say it would be more likely that non-empathetic conservatives would work pretty relentlessly to relocate homeless out of their communities rather than just ignore and co-exist with it.
I am not saying they would solve it, but they would make it some other community's problem.
Ok, but that is a different thing than a specific political lean. I know quite a few folks who claim to care about the homeless, but those claims don’t ever translate to action. That leads me to suspect that what they actually care about is people believing they care about the homeless.
See also: Why US presidents present as happily married and religious, no matter what the reality is.