All valid concerns, but the fact is if you accept the weapon and anything happens, you are at fault.
We've had people get issued, and immediately, check and clear their weapon in the presence of an armorer in the bucket, and get in trouble for it misfiring, despite the fact that it should have been checked and cleared prior to change of hands and in addition to the fact that you hadn't been issued ammo yet. It's dumb, but people die over this, so they are very strict, even when it sometimes seems unnecessary.
Pagers are not guaranteed to be 1 way comms and bringing them into secure locations is a security violation. Additionally, depending on the classification, no unauthorized and undisclosed devices of any kind would be permitted, including any electronics or electronic media such as tapes, CDs, discs, etc. Even when I was issued a verified 1-way pager, I was specifically briefed I was not permitted to bring it into a classified location. Most of the highly classified SCIFS are shielded anyways, you can't use it inside so it's safer to leave it out, along with all other devices.
If your organization allows it, then (if federal) they are breaking the law and should be reported/up-channeled. If it's corpo, you should bring up additional concerns with your security team.
Edit: Also, it goes without saying, current events are probably a good reason why pagers (and other devices) aren't allowed in classified areas. While most focus on disclosure (getting out), we must not forget the risk of data/operations getting destroyed.