Probably not the parish as a whole, but he has a duty to defend himself and his family.
That’s where the rub lies then, if the Parish has a policy for no concealed weapons on church grounds, who is in authority?
Well, how exactly do you define ‘minimal training’?
How many people do you know who’ve ever had a gun pointed in their direction? I know none. My concern is how someone who has a concealed weapon would react if some nut came in brandishing a weapon. They get no mandatory training in crisis management, like what is the job of the police or military. Can they shoot straight under stress? CCW training doesn’t address such circumstances, does it?
I guess that if you feel secure enough in your parish and in your personal circumstances, then don’t carry a gun.
Duh.

I really don’t want others carrying a gun into mass either, at least in my parish.
But others have different security needs, perhaps they are being stalked, we do not know. But they would have a duty to themselves and to those in their charge to be able to defend themselves.
And since what they are doing is not immoral, perhaps it would be best not to judge their actions to an extent greater than the Church itself does. Does that sound agreeable?
Sure, as long as someone with a CCW does not put myself or family at risk with an errent shot. That’s mainly my concern, I guess, that some well-meaning pistol-packing Pete who couldn’t hit a barn door under such a stressful condition ends up shooting someone unintentionally. I don’t have a great deal of faith in civilians being able to handle crisis situations in a house of worship with a firearm. That’s my main premise.
Generally speaking, if you encountered such a person, you would probably never even know that they had a firearm. They are, by definition, concealed
So no need to worry.