Under what circumstances, if any, is it appropriate to tuck the blue jeans into the boot, instead of having the jeans come down over the boot? Help educate me in the wild ways of western wear, por favor.
If you’re in rattlesnake country, I’d suggest it. Along with a lining of fine-mesh chain mail or hardware cloth.
I’ve been wearing boots for decades and never gave this a thought. Appropriate? When stomping around snow, slush, mud, and animal pens (particularly animal pens) I tuck in to kept objectionable glop off my jeans. Otherwise, leave 'em out.
Do people really get very concerned over this?
If you are trying to be fashionable in the city, wear them inside your pant legs.
If you are trying to be fashionable in the country, don’t. Boots are made for working and that’s just what they do. Wear them as if they were safety boots.
If you are trying to be fashionable in the army, don’t. It’s an oxymoron.
If you are going boot-scooting, wear your pant legs out so you can show off the fancy stitching. Of course, if you were a real cowboy you wouldn’t be going boot-scooting: cowboys don’t dance. Unless it’s with their horse. Never get between a cowboy and his horse. 
Can you say “dork”?
I may have read boofy’s post wrong. My wife worked at a western wear store for a couple of years, the term dork is used for anyone that tucks in their jeans insided their boots. Maybe those urban cowpies, er, cowboys from New York tuck in their jeans, I have never seen it done.
It depends on the heighth of the boot top. If the boot in question is a short topped roper style or anything with less than about a 12 or 14 inch top wear your pants on the outside. If you are sporting a boot with a tall top, say 18" or so, then it becomes a huge pain to wad your pant leg up around your knee, bend your knee, pull on your boot and then work the pant leg back down over your boot top. Its just a whole lot easier and faster to pull the boot on over your pant leg. Thats the way it works in the cow country of New Mexico and, as always, your mileage may vary.
Then I guess most of the ranch hands & cowboys handling cattle in Cherry County and the Sandhill region are a bunch of dorks. I just suggest that you don’t do it in Valentine, NE.
I think it’s more of a regional thing than anything else.