I think the safest answer to your questions cjwils is, that it depends. Did the range go all out and purchase the best coverage possible, with the least amount of exclusions, or did they get the bare minimum coverage required?
I stumbled across this in a google search for 'insurance coverage for shooting ranges':
https://www.phly.com/products/shootingrange.aspx
Take a look at the Range Application in the supplemental column. There is one question in particular that I noticed which would answer the question about a customer being injured. "Are shooters required to sign liability waivers?"
Most members or customers may already be required to sign such a waiver, which in effect removes that persons ability to sue for damages. That's not an unusual thing. I have seen concert venues require those in attendance to sign waivers, and virtually no one actually reads them before signing.
As for theft, one might assume a ranges policy would cover it if they have the 'Crime' Coverage on their policy. But that is typically covering the business against crime/theft from either their own employees, or Joe Methhead. Its possible they might buy the coverage that applies to their customers or members.
There are a lot of things any business will say they require customers to do, or not do, and will say its their insurance companys rules. Sometimes its true, sometimes it isn't. Any business that wishes to remain profitable will do whatever it takes to reduce the risk of having insurance claims filed against their policy. Have you ever been to a bar, and seen someone do something extremely stupid like climb on a table and start dancing? Bar staff will normally tell that person to 'get down! I said get down! you cant do that! Because of our insurance!" Theres no exclusion in their policy that says "we will not provide coverage to anyone dancing on a table". But the business wishes to reduce the risk of someone hurting themselves so they will say the policy against dancing on tables is due to their insurance coverage.
One bar I worked at, had a walk through done by the insurance retail agent, not a representative of the actual insurance company, and not someone authorized to inspect the bar or its procedures, but as soon as they retailer observed the bouncers all carried handcuffs, they immediately told the bar owner 'your policy will get cancelled if your staff uses handcuffs'. Total Bee Ess! But I imagine a range would get similarly told 'Your policy could get cancelled if your members are allowed to practice quick draws!"
And there might be good reason for that. Maybe the company does insist that dangerous behavior be prohibited? Maybe they don't.
Like I said, it all depends!