Instead what we get today is a reduction in income for a capped amount of charitable giving. Depending on your tax bracket this doesn't even approach a dollar for dollar credit. What I can promise is that $10,000 given to a soup kitchen, shelter, or to pro-bono medical and legal services in your area go a LOT farther to helping those who truly need it than that same $10,000 that goes to the federal government.
The percentage of money that is actually spent on services for the poor with the vast majority of charities is higher than the percentage of the money budgeted for similar services that actually make it to those services in government.
You may discover hypocrisy but you may also awaken a sheep.