The conservative justices unfortunately seem inclined to side with the city in this case. Their questions seemed unsympathetic to the people involved and they seemed inclined to let Grants Pass do what it wants, as long as it doesn't go too far. But the liberal justices rightly were more concerned that Grants Pass and every city could begin a banishment race to push homeless people out of their jurisdictions.
The conservative justices aren't being cold-hearted, they're being realistic. The lower-court ruling limiting how cities could manage their homeless problem wreaked havoc on the municipalities and made it unsafe for people to enjoy public recreation spaces. It's possible to be sympathetic to the homeless while also realizing that permitting bad behavior is harmful to society.