I have no objection to dry aging different meats in the same fridge, but I usually only buy one lamb at a time and perhaps a random whole muscle of beef (like the whole eye of round). I never dry age a muscle that has been cut into because I like the results with the outer membrane intact.
I do not age organ meats, but I might hang some organ meat for a few days while I eat a bit each day.
I don´t really enjoy muscle until it has been aged a week, and after about 6 weeks, it gets too tough and dry, so I limit my purchases to what will get finished in time. I have read that most of the dry-aging changes occur within the muscle structure of the meat, not on the surface, so I never considered external bacteria to be a major factor. (I could be totally wrong about this.)
Also, as you can see, I don´t go crazy with variety. What is sold as ¨game¨ here is ranch-raised, and my son hasn´t been hunting for a while.