I don't think that's a charitable way of interpreting the comment.
Mormons as a rule are very generous with the church, and often with church affiliated charities. If the deduction for charitable giving was removed, the Mormon church would do fine, and likely so would many of their charitable activities, and it would seem more like separation of church and state to me.
If the charitable giving deduction were removed, I guess I agree that at that point there wouldn't be a way to argue (from a constitutional perspective) against Mormons in Utah voting for low levels of government support.
As it happens, I'm not convinced the "all charity should be provided by religious institutions in Utah" narrative for Utah voters is actually accurate; Salt Lake City at least is fairly generous with the homeless, at a government level.