My understanding is that UDT is not actually computable. As a result, no possible agent can act as you describe. So this doesn't seem like a particularly compelling thought experiment.

Are you confusing UDT with AIXI? It is certainly possible for an agent to act as described and the tricky part isn't anything to do with "UDT" (but rather the possible but difficult task of making the predictions.)

What's the case where I actually care about non-causal interactions?

The case given is sufficient. Anyone who is capable of one-boxing on Newcomb's problem will, if consistent, also cooperate with agents that cross out of the future light cone based on utility maximisation grounds given the payoffs described. If they either two box or defect then they are implementing a faulty decision algorithm.

For an example that doesn't include any potential exploitation of loved ones see Belief in the Implied Invisible.