My mom with mild/moderate Alzheimer’s has started saying things have been stolen from her apartment in assisted living. What to do?

Unfortunately, the mother who raised you to not jump to such conclusions is not the mother you have now.

Accusations are very common with AD. You've found out, probably the hard way, that correcting someone's pseudo reality only causes conflict. You're right in not arguing with her. Accusations, delusions, hallucinations are all difficult for a caregiver to respond to. Mom isn't going to change her reality so you have to change yours. In the case of accusations, you might respond with, "I'll talk to the staff about it", or "Yea, I know. The staff caught a visitor stealing". Some may balk at being less than truthful, but it's not about truth, it's about validating her concerns.

There really is no good way to handle this. Assure her that there is no money left in her room, hence nothing really to steal. My brother stayed so "with it" the time he had still to live with his probable early Lewy's dementia. Yet it was this paranoia about others stealing from him, entering his rooms without permission, that troubled him the most. I basically repeated to him back the time I was accused and could do NOTHING to prove I had not done what accused of, and that I would NOT see him accusing another in this way. The very sad thing here is the fact that we tend not to believe our elders, beCAUSE this is so common, makes them prey to people who "may" attempt to take things from them. I don't have an easy answer to this one myself. When my brother found the money he thought stolen, in a white towel tucked away BY HIM in his closet, he didn't tell me. The way I found out was a bit comical, but I read him the riot act. He told me he was afraid that they would think him senile and lob him on over into memory care; I told him I didn't want EVER to hear about missing money again, that he was well aware money was NOT to be left in his room other than in a bolted safe, and if it got left in his room otherwise, in my book they were welcome to it. We never bickered but we had a bit of a go-round over this, and it didn't happen again. He was likely "afraid to tell ANYone " such a thing again.