This has been bugging me for a long time, so I've been testing different scenarios. If all my Sims in my household have the Player trait, they can do anything they want with each other and do not generate jealousy or sadness. If I create another household and they all get the Player trait, same thing. Now, if any members of these two households get together, in theory, no one should get jealous of any romantic interactions, since they all have the trait.
However, when romantic gestures are initiated or reciprocated by the guest sims, it seems their Player trait is not being recognized. My active household sims get jealous if they had a romantic relationship with that guest. Then, it seems that once that guest sim's Player trait is "broken", it doesn't work any more, even when I play that sim's household,