You are talking about Federal income tax, but everyone pays usage taxes. Poor people buy booze, cigarettes, gasoline, and everything else that gets taxed at the transaction and before. And all of those taxes are regressive, in that they take away a larger fraction of a poor person's wealth than a rich person.
Entitlement spending is mostly social security and medicare/medicaid. It is not housing and food, which by the way, goes right back into corporate coffers as soon as it is doled out. That's the real reason we have food stamps. All that money goes straight to Walmart and the handful of giant corporations that control our food supply as soon as it gets spent. They are the ones with Washington lobbyists, not the poor people. Hating poor people is just a distraction from the reality that the welfare state exists for corporate benefit. They are the ones who wrote the rules, like the one that says I can buy diet soda with food stamps. Who the hell is benefitting from that besides the soda company? Diet soda never kept anyone from starving to death.