This isn't specific to the Recycler trait. I have a social club consisting of 7 members plus my Sim. None of them have the Recycler trait as they were created weeks before the Eco Living pack was released and they have been members of this club since they were teens, which is when their last personality trait was assigned.
I recently moved my Sim from one house into another. The Welcome Wagon showed up and one townie went straight from the front door to the computer and swiped it. I assumed she had the Klepto trait so I asked her to leave and instead started a club gathering. The first person through the door swiped a kitchen counter. The second person swiped the computer I had just replaced, the coffee table, and then went into the kitchen to swipe another counter. The third swiped a couch and a chair. The others went down to the basement where two love seats and a stereo disappeared. This was all within about 2 minutes of their arrival. I ended up exiting the game without saving!
The only connection my game had to the Recycler Trait was a girlfriend of my active Sim who had it but I got rid of her after she swiped their sofa. At the time I thought that was an intended consequence of the trait, which I wasn't prepared to deal with so I had them break up. But more importantly, she was already out of the picture and had never stepped foot in this new house when all the swiping took place during the club gathering, so that can't be connected to her. Also of note, I'd had several club gatherings in the old house without anything going missing except the sofa that one time. It wasn't until moving to the new house that the swiping has become constant.
