This isn't about everyone, just certain segments within the 2 general types. Firstly, the non-religious, if they don't think about, or take their non-religion seriously, are open to anything. They can give freely, without boundaries of what to give to. Secondly, some, if not many, religious people have a boundary, and that boundary is their own tribe. So if there are two charities, each run by different religions, the non religious person can give to either, but the religious folks feel bound, or are bound to give to their tribe only.
If we use countries as a hypothetical analogy, a person not bound to a country could designate his taxes to an impoverished country.
In the other similar thread, the idea that the non-religious could be more helpful wasn't given as a possibility. So I changed my vote to 'this poll doesn't reflect my thinking'.