It depends. I only rinse where I think not rinsing risks the foxes going through our bins, or getting maggots, or it smelling in hot weather. So Nutella jars get washed, for example. Plastic trays that ham come in where every scrap has been eaten - no washing.
On the whole I try not to waste much water or soap washing recycling. If I can get away with not washing I will leave it. We are a family of five and put a tiny amount in our black bin - we generate huge amounts of recycling and cleaning all of it would be a huge task. ‘Just put it in the dishwasher’ like there’s ever going to be lots of space in our dishwasher!!
We are currently running at two green boxes (plastic) one large cardboard box filled with cardboard, one black box (paper) and two brown boxes (food) every week. Note these are boxes, not bins, but still, it’s a lot! It would waste a lot of water to wash all the plastic just to be ‘safe’. I presume the recycling plant must have a rudimentary rinsing system, not having would be ridiculous.
OP, if you are trying to persuade your sister, point out that in this weather anything with food left in must surely be getting a bit stinky...approach it from that angle (reducing house smell, risk of foxes) rather than arguing about the processes at recycling plants.