"If there is a cheap but not completely free way to signal that you have the disposition of a moral, trustworthy person, for example by rooting for the underdog in faraway conflicts, then we should expect people to have the trait of displaying that signal."

During the time span when the underdog tendency was presumably evolving, I doubt that there was any awareness of far-away conflicts that didn't touch the observer. Awareness of geographically distant conflicts is a relatively modern phenomenon.

Here is an alternative explanation. The inclination to protect the weak from harm provides reproductive advantage--parents protect their young who go on to reproduce. This tendency is thoroughly bound up with empathic responses to distress signals from the weak and defenseless. It's the default position.

This strategy works up to the point when the aggressor poses an overwhelming threat. Challenging that big silverback when he's killing someone else's young could buy you a heap of trouble--better to form an alliance for one's own safety and the safety of one's young who can go on to reproduce if they survive). So, when the cost is low we're inclined to feel empathy for the weak--it's the default position. But when the threat is more immediate and overwhelming, we identify with and seek alliances with the aggressor. Nothing about signaling our moral standing to others is necessary in this formulation.

Clearer, but I remain unconvinced. The value of this signal, as you present it, seems to provide so little real benefit that I can't distinguish it from the noise of random mutation.