Limits of, or preconditions for of Blue-Green deployment?
I must admit that I don't quite get the examples your giving. Sure, random numbers will be different between the two environments.

Blue-green means simply to have two nearly identical production environments with some kind of router/load balancer in front. Clients talk to the load balancer, and the LB routes requests to one of the two environments.

To deploy a new version, you provision all machines/services/etc. in the inactive environment, test to your heart's content, and then do the instant switch (on the router) if you're satisfied.

Actually, I don't see anything that requires any precondition at all about this. Obviously, one precondition is that you are at all able to create a second, fully fledged production environment in the first place; and that there is a technical solution that works as a load balancer in the above sense. That may get very complicated if you have a widely distributed system which you want to switch completely at once. That may just become to complex. 

But aside from that, nothing special compared to, for example, running a separate test environment next to your dev/prod environments.