There is at least one study disputing that interpretation:
Voluntary contributions from individuals are the lifeblood of nonprofit organizations, which in turn fund a large portion of social services in the United States. Given this reliance donor generosity, it is important to understand who contributes, and to where. In this paper, we argue against the conventional wisdom that political conservatives are inherently more generous toward private charities than liberals. At the individual level, the large bivariate relationship between giving and conservatism vanishes after adjusting for differences in income and religiosity. At the state level, we find no evidence of a relationship between charitable giving and Republican presidential voteshare. Finally, we show that any remaining differences in giving are an artifact of Republicans' greater propensity to give to religious causes, particularly their own church. Taken together, our results counter the notion that political conservatives compensate for their opposition to governmental intervention by supporting private charities.
However, note that this adjusts for "religiosity". So what they seem to be saying is that conservatives/Republicans give more because they are more religious, not because they are Republican or more conservative. So in other words, they found the same relationship as Brooks but counted it differently. Whether you call this insightful analysis or sophistry is probably going to be heavily influenced by your own views.
The link in the question is citing the work of Arthur C. Brooks, a professor at Syracuse University, who wrote Who Really Cares: The Surprising Truth About Compassionate Conservatism. This article by conservative columnist George Will cites some of his findings, including:
-- Although liberal families' incomes average 6 percent higher than those of conservative families, conservative-headed households give, on average, 30 percent more to charity than the average liberal-headed household ($1,600 per year vs. $1,227).
-- Conservatives also donate more time and give more blood.
-- People who reject the idea that "government has a responsibility to reduce income inequality" give an average of four times more than people who accept that proposition.
Note that the statements in the article mix findings from examining state level data with results from polls. Presumably Brooks' book gives more detailed citations.
One reason why I included these is that they directly dispute the assertion that conservatives give more as a percentage of income because they are poorer. As the first factoid shows, conservative households give more in raw dollar terms even though they have lower incomes. As the second factoid shows, conservatives give more in non-monetary resources. Note that this doesn't dispute that these things are more true because of religion than political partisanship. But "religiosity" itself is predictable from political partisanship.
Another source. Again, they find that religious people give more and conservatives/Republicans are more religious than liberals/Democrats.
TLDR: The statistic is real but the interpretation can be contested. Religious people give more. Conservatives/Republicans are more religious. Conservatives/Republicans give more (because they are more religious). All statistically true by every source that checked. Subject to different interpretations.