Well, "good clean christian fun" is just a saying, not indicative of shooting varmits as something the church has anything to say about.
No, you don't eat prarie dogs. Yes, they are a royal pain in the ass, causing many, MANY horses to be put down or crippled by stepping in the damn holes, not to mention the crop damage issues.
I shoot them at the Western Canadian Rodeo grounds, some guys I know are in charge of the gopher control, hence I get to shoot a lot of them.
Also, I use iron sights and even pistols to shoot them, not only scoped rifles, but a scoped .17hmr or 22-250 is the best rifle and caliber to shoot them with in terms of cost per elimination of problem.