Given this unfortunate state of affairs, I suspect it is actually a better idea for most utilitarians to commit themselves to a policy like "Don't steal someone else's partner" rather than attempt to do the math every time they are faced with the decision.

See the paragraph that follows on second order effects. In the context of flirting with people in clubs, rather than attempting to break up established relationships, the policy of "don't interrupt someone else's flirting" is probably suboptimal.

(Did you not think that paragraph explained the point? Should I have put the asterisk up higher? I'm confused why you made this objection to what you did, when a sibling comment engaged with my discussion of second order effects directly.)

Of course, there may still be times when its just blindingly obvious that the math is in favor of stealing, in which case screw the policy.

The primary reason to have a policy like this is because you trust your offline math more than your online math, in which case if the policy doesn't have a clear escape clause you reasoned through offline, you should trust the policy even when your online math screams that you shouldn't.