As the example suggests, Brooks is concerned with support for what he calls "forced income redistribution to achieve greater income equality," (p. 181) not things like same-sex marriage. So from now on I'll refer to opinions on redistribution rather than "liberalism."
In fact, the GSS never had the item he described. However, it did ask for a response to "It is the responsibility of the government to reduce the differences in income between people with high incomes and those with low incomes." The numbers on that question pretty much match those that he reports. People who strongly agreed gave an average of $64, people who strongly disagreed gave an average of $542.
The GSS has several other questions about attitudes to income redistribution. One goes: "Some people think that the government in Washington ought to reduce the income differences between the rich and the poor, perhaps by raising the taxes of wealthy families or by giving income assistance to the poor. Others think that the government should not concern itself with reducing this income difference between the rich and the poor. Here is a card with a scale from 1 to 7. Think of a score of 1 as meaning that the government ought to reduce the income differences between rich and poor, and a score of 7 meaning that the government should not concern itself with reducing income differences. What score between 1 and 7 comes closest to the way you feel? " People who chose 1 gave an average of $87 and people who chose 7 gave an average of $208. But people who chose 4 were way ahead of both, with an average of $506.
The problem with giving the averages is that the distribution of giving is extremely skewed--most people report giving nothing, while a few give very large amounts. In a sample of about 1,000 people, the top ten people gave almost half of the total. So apparently impressive differences in the means can reflect a handful of people. So I'll give t-ratios from an appropriate model for skewed dependent variables (controlling for income). With the first question (GOVEQINC) the t-ratio is 2.6. With the second (EQWLTH), it is 0.6. The usual standard for "statistical significance" is a t-ratio of about 2. Some people would set it higher and some lower, but everyone would agree that 0.6 amounts to no evidence either way--the variable might make a difference in one direction, the other direction, or no difference at all. So your conclusions about whether attitudes to "forced redistribution" are related to charitable contributions depend on which measure you use.
It seems to me that EQWLTH is better in principle because it simply asks what the government should do. Some people might interpret EQINCOME as implicitly choosing between individuals and the government--in effect, asking if the government has the primary responsibility. That would make the association almost automatic.
The GSS has still another question on the same general issue: "On the whole, do you think it should or should not be the government's responsibility to . . . reduce income differences between the rich and poor?" People who say "no" give more, and the t-ratio is 2.2. That question (EQUALIZE) doesn't seem open to the same objection as GOVEQINC. So now we're back to conclusions differing depending on which measure you use.
EQUALIZE is part of a series asking about the government's responsibility to do various things. The questions and the associated t-ratios (positive numbers mean anti-redistribution answers go with more charitable giving):
Provide a job for everyone who wants one. 2.8
Keep prices under control. 2.3
Reduce income differences between the rich and poor. 2.2
Provide health care for the sick. 1.8
Provide a decent standard of living for the unemployed 1.1
Give financial assistance to college students from low-income families 0.8
Provide decent housing for those who can't afford it. 0.5
Provide a decent standard of living for the old 0.1
Provide industry with the help it needs to grow. -0.1
All of these, except the second and the last, involve egalitarian redistribution. All, except again the second and last, are things you would expect liberals to be more favorable towards (those two are ambiguous--you could make arguments in either direction). But only three (counting EQUALIZE) have a statistically significant association with reported giving, and one of those is the ambiguous "keep prices under control."
Putting it together, the evidence is weaker than Brooks suggests. By luck or design, he happened to report just the one item that gave strongest support to his case. Still, there seems to be something there--some measures of support for redistribution or a more expansive government are associated with lower charitable contributions, and none were associated with more.