Other bits you won't see paraded around much
To be fair, I think that brings up an important point about charity. The reason Utahans give so much to charity is that Mormons give 10% of their income to the Mormon church. I think religious charities may account for a good percentage of Republican charitable giving.
Does giving money to your church necessarily equate to charity? Let's say you're just giving money to your local church. It's somewhere you go once a week and your donations are necessary to keep that institution going. Isn't that more like paying your gym membership? Sure, if you're giving money to your local religious soup kitchen, that's definitely charity. But, giving money to your church is basically a membership fee so a fair accounting would exclude that from the totals.
You can't make a neat separation since most soup kitchens are either run by or hosted by churches. The charitable giving statistics also include all sorts of arts, education and other institutions that are attended in part by the people who give the money to keep them up. So it is not like this issue is unique to churches.
As for the figures being discussed here, is it basically that people are still giving about the same amount of money that they were six years ago, even though some are making more and some are making less - thus leading to changes in the share of income?