If someone offers you a gift and you refuse to accept it, to whom does the gift belong?
Criticism and abuse are like slugs that stick and suck the life out of us. I remember a Tibetan teacher once saying about criticism that either the critic is right about the issue and we need to correct whatever it is, or, as much as we can tell from our perspective, they are misguided and being unfair.
In that case we can have compassion for them. But compassion does not mean accepting their abuse. We have the choice to refuse to accept their abuse.
We can explain quietly in calmer times that we are no longer willing to accept the criticism and abuse and if they choose to offer it we will walk away and allow them to calm down until they are willing to discuss whatever the issue is in a loving and peaceful way. This, of course, may mean making the choice to not engage with that person at all.
We do have a choice and in exercising that choice we build our own resilience and set ourselves free. It's often not easy, but does it not always makes sense?