Of everything he's done with EOs, this might actually be the most legal one.

the President has authority to allocate enforcement resources. "We are going to make sure the law was followed" is that authority. He can dress it up with all the flowery "no political debanking" rhetoric he wants, but if there's no actual law against refusing to hold accounts for the KKK, there's nothing for enforcement to do, and that's that.

(Apart from that, increased scrutiny could of course uncover other kinds of lawbreaking. When we're talking banks? Not against that.)