Do you have to pay child support if custodial parent receives food stamps?

Not to that parent. Any money must go to Welfare, so contact child support enforcement to get the money diverted. If you're paying without a court order, those are not considered child support. see links below

Recipients of food stamps (now SNAP) and Medicaid do not assign their child support rights to the State - this happens only for recipients of cash assistance. In any case, do not give money directly to the custodial parent/obligee unless you're willing to write it off as a gift.