As I see it, we have two very different scenarios here:
1. An armed Security Team that is sanctioned by the church.
The church is then responsible for their actions, as would be their insurance carrier, assuming the church had advised the carrier of the armed Security. If they did not, I am sure the insurance company would not cover an incident.
(I speak with some experience here, as I have owned a Contract Security company for over 27 years, and have been a Private Investigator for over 18 years).
2. Members with carry permits providing Security when they are attending services. They should advise the Pastor or Elders of this, although in some cases that may not be a good idea. Some denominations are very anti-gun. One Protestant one in particular that I will not name. They would probably not allow members to carry. If it were me, I would do so anyway. These members should then keep this to themselves. I know a guy who goes to a large church in another Iowa city. He doesn't have a carry permit, but thinks it's cool. Several members of his church carry at services, and he is constantly talking about it. I have repeatedly told him to keep this information private. Like the guy mentioned in a post above, he thinks it's "cool". He is simply not informed about legal or tactical issues, and unfortunately, he doesn't think he needs to learn any more. Understand, his mindset is what is most common among people who are not aware of the realities of self-defense.

We live in a very dangerous world, and I have read articles quoting very high ranking government and military people saying they expect houses of worship to be attacked by terrorists. I agree. Since 11 September, 2001, I have not been in church unarmed. In the church we used to go to, one of about 150 people, my Pastor and one Elder knew I carried. I actually had people casually ask me if I carried at church, I always said no. (And repented later for lying). We go to a church now that runs about 1,000 on Sunday morning. I am constantly armed, and not with a mouse-gun either. I carry a Glock 23 in my Kramer Confidant shirt holster, with a spare mag, and my M340PD in my left front pants pocket. Nobody but my Wife knows at this point, and that's alright with me.

"Security" in church can take many forms. If it is sanctioned by the church, the operatives need to be trained and they NEED TO KEEP THEIR MOUTHS SHUT! It's part of being an adult.
Or at least that's the way I see it.
Jim