Your New York Times link was behind a paywall, so I did some checking myself and went to another site (Giving Compass, which is fairly accurate about charity donations), which used the same study from the NYT, and found this................
Martin Levine discusses the relationship between political affiliation and charitable giving, revealing a concerning trend of retreat from giving.
givingcompass.org
Republicans do give more, but where that money ends up is not yet clear. One of the study’s authors, Rebecca Nesbit, associate professor of public administration and policy at the University of Georgia, told the New York Times that Republicans prefer to “provide for the collective good through private institutions. But we don’t know what type of institutions they’re giving to.” It also wasn’t obvious “whether donors were being purely generous or whether they would also benefit from their donation. This relationship is called consumption philanthropy, in which people give to a religious organization or a school from which they will derive a benefit in the form of, say, a better religious education program or a new gymnasium.” Giving to a food bank or a homeless shelter has a very different outcome than does giving to a private school.
So................the question is, are they giving to charities to help those who really need it, or are they giving to their own favorite charities or private institutions that help THEM (the people making the donations) out? If they are giving to charities that enrich their own lives, then there is a selfish motive involved. Not everything is a "one size fits all", especially when it comes to charities.