Why do caregivers allow abuse?

You and your deacon said it well. People do not have to put up with abuse. The problem is that guilt enters in. People wonder if it's their fault the elder is acting up (it can be, but generally isn't). They know the elder is sick so they try to be patient. And the biggest reason of all - they are still (unsuccessfully) trying to "earn" their parent's love.
While it's good to be introspective and see if our responses are making our elders' issues worse, when there is actual abuse, or when there is a situation like the deacon's, the appropriate thing is generally to take steps to get into separate living arrangements, and to set boundaries. Many people could use counseling by someone like your deacon who can help them through these tough decisions.
Take care,
Carol