Universe B is quite literally the opposite version of Universe A. So much so, that everything in Universe B is in fact made of antimatter.
Antimatter is perfectly harmless with itself and behaves exactly like ordinary matter (other than the fact that they have positrons and antiprotons instead of electrons and protons). However, we all know that matter and antimatter don't mix: when such particles interact, they violently transform into pure energy.
So how can people from Universe A use the mirrors to explore Universe B? Well, the mirrors are more than mere portals between universes. A better analogy would be an airlock. Crossing the mirror from A to B applies a magical "antimatter shielding" to each individual particle, such that they behave exactly like antimatter particles.
When returning to Universe A, the shielding is stripped away and the ordinary matter behaves ordinarily once again.
Unfortunately, the mirrors were developed with this explicit "A $\rightarrow$ B = wax on", "B $\rightarrow$ A = wax off" rule. Therefore, if anyone or anything from Universe B tries to cross into Universe A, the mirror won't be able to place "matter shielding" on them... to horrendous effect.
Now, you can choose how secure the mirrors are regarding Universe B objects.
- They can be dangerously unsecure, such that objects and people CAN cross, but there are just rules forbidding it for the simple reason that if anything were to cross, it'd be the equivalent of multiple nuclear bombs the moment they crossed.1 This would be the equivalent of the mirror going "oh, this object has no shielding to wax off, so ignore it".
- They can be secure, forbidding non-shielded (anti)matter from crossing back into Universe A. You can also choose how severe this security feature is:
- It may be harmless to those attempting to cross: the mirror momentarily shuts down as soon as the first non-shielded molecule attempts to cross1
- It may be harmful: the mirror allows the molecules to enter,2 but upon detecting that they are unshielded, destroys them. So if someone from Universe B puts their hand through the mirror, they'll no longer have a hand.
- It may be lethal: the mirror allows entire objects/people3 to enter before determining whether they are unshielded. If so, the entire object/person is destroyed.
Later on, this problem is somehow overcome, such that people from Universe B can cross over to Universe A.
As others have suggested, this may be by people from Universe B developing their own mirrors. This would imply that members of each universe must use different mirrors.
Another option is that someone figures out how to "hack" the original mirrors to allow passage. You can once again decide how easy or hard this is:
- They just had to change the mirror's behavior from "A $\rightarrow$ B = wax on", "B $\rightarrow$ A = wax off" to "unshielded = wax on", "shielded = wax off". This implies that the antimatter shielding for ordinary matter can be trivially repurposed as ordinary-matter shielding for antimatter.
- They had to develop shielding suitable to make antimatter behave like ordinary matter, and then make the mirror's "code" more complex: "if A-matter, A $\rightarrow$ B = wax on antimatter shielding, B $\rightarrow$ A = wax off antimatter shielding; if B-matter, B $\rightarrow$ A = wax on ordinary matter shielding, A $\rightarrow$ B = wax off ordinary matter shielding".
1 (yes, this footnote appears twice above) Some magic handwaving will be needed to explain why random air molecules from Universe B aren't a problem (either generating massive heat on the Universe A side or causing the mirror to constantly shut down). Or just ignore this point.
2 Note the word here is "enter", not "cross". This implies that the mirror isn't a door, but a bridge between the two dimensions, such that objects actually don't go A $\rightarrow$ B (or vice versa), but A $\rightarrow$ mirror bridge $\rightarrow$ B. The travel between both ends can be virtually instantaneous as far as anyone is concerned, but this bridge is the "safe zone" where the unauthorized unshielded antimatter can be safely destroyed before it can enter Universe A.
3 Some more magic handwaving (or authorial ignoring) will be needed to explain how the mirror identifies what constitutes an "entire object/person".