Regarding the idea of Washington taking into account posterity when considering his actions, the author seems to use this as a way to say, "Well, Washington wasn't being totally selfless here."

Which is true, but at the same time, totally besides the point. We collectively seem to understand that if I help an old lady across the street in order to impress a pretty girl that's watching, I wasn't being selfless. But if I did it because I thought it was going to help me get into heaven, is that still a selfish act?

Ellis refers to Washington seeking "secular immortality." Washington, from all the evidence, didn't believe in an afterlife, but he did understand he was going to be immortal in another way–coins were already minted with his face when he was president and before his death Washington DC was already nicknamed Washington. He knew what was coming.

So is it that bad that he thought, "I wonder how I will be judged by future generations for this action?" Maybe it's not strictly "selfless" but I think we'd all do pretty well to ask that question every so often.

It's actually very similar to what I call The Grandchild Rule that I've heard somewhere (but can't attribute). "Don't do things that your grandchildren will wince at." Or something like that. No, you can't always know for sure. But a lot of things wouldn't pass that test.