The USPS doesn't pay taxes. That means that we are paying their taxes.
No it still doesn't, You're not paying the Catholic church's taxes in the exactly the same fashion.
Not entirely true. While they don't collect funds collected via taxes, they also don't PAY taxes on many things, like say property taxes for their offices, sorting facilities, etc. So they indirectly are Government funded, at the state and municipality level.
So they're funded in the same way religious groups and non-profit organizations are funded by the government.
How could you be any more private than by being the only user of Google+ ?
Being the first person to like Slashdot Beta.