Not too long ago and not to far away, there was a place where everywhere homeschooling parents were considered criminal and punished by law.
But, heroic people got involved in politics and low and behold the evil dragon of educracy was driven away, and homeschooling is legal just about everywhere and even now respected.
It is true that vouchers would increase the reach of government into some private schools -- and appropriately in some regards. We do not want to give tax dollars to schools espousing Islamofascism.
What more than makes up for this concern, however, is that it vouchers vastly increase the reach of the market, parents and general commonsense into the public schools which now miseducate the large majority of our children.
I unabashedly support vouchers.
And if you really fear what might happen to your private school via vouchers consider what the homeschoolers did and realize that if you are politically vigilant government's role will not become unduly intrusive.
Most of us homeschoolers don't want gov't control in any way - including gov't funding. Homeschool organizations often fight against gov't tax credits or funding of any kind. We don't want the gov't's foot in the door.