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This is a bit of a reach but bike lanes are most effective when they connect directly. That means they are built on major roads, not cul-de-sacs that go nowhere.
Who buys roads in front of major roads: the poor. Because the expensive homes are in cul-de-sacs far from the heavy road noise.
So the law is equally just to rich and poor in the same way it is equally just to rich and poor by making sleeping under a bridge illegal.
Everyone benefits from the bike lanes, but only the poorer homeowners are inconvenienced.
The reason they complained wasn’t specifically the bike lanes but the loss of parking which affects them and causes a ripple effect on their neighbors. Adding parking fixes the overcrowding that the bike lanes caused.