RAT has NOTHING to do with your players getting a freeze when opening their backpacks. The fact that you have a mod that is adding new items or otherwise changing what happens to inventory is probably the problem.
I get that the mod works fine without RAT. But what it sounds like is all of these new items have to be indexed by BCM, and if there are that many items, it might be what's causing the issue. Maybe there is something StompyNZ (The author of BCM) can do about this, but I can't even say its a problem with BCM. You'd need to contact him and see if he can help you out. Or, its the mod that is adding in all of the items, doing it in a way that might be causing issues. I don't know, as i don't use that mod (or any other mods than BCM and Allocs, which don't cause this issue with any other mods (that anyone has reported at least)).