Wanted to offer you some more info to make sure we are not confusing you as both comments above seem at odds, and I don't think they really are. The Caribou synthetic bags do breathe, they do allow some air exchange, aka breathing. Are they as easy to blow through as a cheese cloth bag, not a chance. So in comparison to many bags they don't seem to breathe nearly as well. As WB alluded to, a high degree of breathing is probably not really that important.
You asked the right question, do they breathe enough? What you need is a bag to protect your meat and allow it to glaze or crust. These bags, in my experience, do just that. They dry quickly too, so I suspect there is a wicking of moisture away from the meat effect too, which cotton mesh high breatheability bags won't do so well. Somewhat like a good base layer we may use while hunting, I suspect.
So for their intended purpose, they breathe fine, and you do want a bag that breathe's, or whatever you want to call it. Are they real easy breathers, if that is even a concept, nope. You would not want an impermeable barrier to moisture/air, like a plastic garbage bag, which would not breathe at all. Hope that helps clarify the breathing function. I am sure you will love a good set of synthetic bags, I love mine.