Is it safe to wash meat packaging before throwing it away?
Rinsing or washing the container is no worse than rinsing or washing a plate on which you have let your meat rest. But do it when you take your meat out, not a couple of hours later, to avoid spoilage starting.
If you send yours to landfill, cleaning it is for your comfort.
Where and when I grew up we would never bother, but we did accept that bins smell of spoiled food. If you want to keep your bin from smelling you may want to clean it.