Jesus did it.
He told his followers to do it, too.
Paul reminded early Christians that they are “subject to governing authorities,” and as such, they should pay taxes as a matter of conscience, and not just to avoid jail. For more, go here or here or here.
In the Hebrew Scriptures, required tithing was something like a tax, though the Hebrews mostly paid in animals, not money. (Imagine how messy that would be, all of us rushing to the post office this evening with our goats and doves.)
So pay up, buttercup, even if you don’t like where your tax dollars go. (Check out this chart from National Priorities Project for more on where your 2015 tax dollars will go.)
Dating Jesus 
If paying taxes is a matter of conscience, as Paul, (the Tax Collector turned self-styled Apostle), claims, why do Christian organizations insist on exemption?
And if Christians are to submit to “governing authorities,” as Paul pronounces, why do they insist on exemption from government laws? (Think Contraception Mandate for starters.)
Jesus really didn’t pay the church tax, did he. Somebody else paid it for him.
The whole Render Unto Caesar thing has been beat to death, I know. (There’s a link missing in there at the third “here.”) But when considering the modern day Caesar, representative democracy, (or what passes for it these days), is not dissent, including tax resistance, as much part and parcel of meaningful participation in government as paying taxes? Archbishop Raymond Hunhausen thought so in the 1980s when he withheld half his federal taxes to protest nuclear arms proliferation.
I don’t think it’s clear how Jesus would have responded to the regressive taxation practiced in the United States. Burdening the righteous to support the hypocrites just doesn’t seem part of his agenda at that time.
I do not know how it works out that religious institutions don’t pay taxes. For Christians, at least, it runs counter to their Book. As for Jesus’ reaction to our current tax situation (the rich get richer and the poor, well…), I think you’re right. He’d hate it.