No, she's saying that taxing churches, which by definition are non-profit, would end up wiping many churches out of existence.
I don't think it would. I don't think people understand that gifts are not taxable unless they are over a certain amount.
The reality is that people would no longer receive a deduction for their charitable contribution. I don't think that would make them stop giving.
But if it did, that would only cause the government to give more. So in the end, the government would be paying 100% of the "charity" instead of giving a tax break on say 20% of the charity.
I think it is an emotional thing. They hate religion so much they can't look at it analytically.