I question your probability argument that concerns around guns are irrational.
Just because heart disease is the most common cause of death doesn't mean concern about anything else is irrational.
I think being afraid of something that can kill you is absolutely rational.
> All of which are vastly more likely to happen than being shot, which itself is an order of magnitude more likely than an innocent person being shot.
If fear of guns is irrational then why do licence-holders need them?