Change the subject question to: "Should I be able to have sex at the taxpayer's expense?"
Everyone should answer no, haha.
It has nothing to do with 'having sex at the taxpayer's expense'. The sex may be paid, or free, or have emotional costs, but in any case all of these are paid by you. The state should merely provide medical care, for obvious reasons. Public health is not an individual matter, but rather one of managing things like pregnancy and transmission of various diseases through the population. A society with provision of free medical care, free STD treatment, and birth control methods will be a much healthier one.