They’re all in different conferences. But this is a case for
@Big McLargehuge
To put it bluntly - they're the main show for hours in any direction playing the most popular sport in the region/country. In places like Missoula and Bozeman those teams
are the live entertainment scene.
The Montana schools are a solid ~10 hour drive from a major professional team and basically everyone of importance in the state went to one of the two schools, so they're constantly in the spotlight. The entire state shuts down for Griz-Cat/Cat-Griz week.
I can speak less intimately to the Dakotas...but they're basically in the same boat, just quite a bit closer to the recruiting grounds of the Big Ten. They're the FCS equivalents of Boise State. You take highly motivated kids and give them an opportunity and quite often it'll work out nicely.
To put it another way...as someone who grew up in Pittsburgh - people in Missoula were far, far,
far more likely to be Griz fans than people where I grew up were to be a Pitt fans. They hold a place in the hearts of people in the region more akin to the hold Penn State has on Central Pennsylvania. Bozeman is much the same. They are the best show in town, which only further strengthens their appeal and strength year after year, generation after generation. No major professional teams are going to come close to these markets, so the colleges default into that role.
Basically if you shrink Alabama and ignore the cultural differences, you get Montana. At least in regard to college football. Griz-Cat is an HO scale Alabama-Auburn.
You can't be a star playing for Duquesne, but Montana or Montana State? You better believe every other car dealer, insurance salesman, or state senator in the state played for one of those two schools.
I believe the Dakota's along with part of Montana are in the Great Plains region. Isn't Minnesota considered part of the Midwest?
I have no answer for your first question and have wondered the same many times.
I mean...yes to all of that, but with conditions on everything.
'Midwest' means different things to different people. People use that term to describe my hometown of Pittsburgh, which makes slight geographic sense but little cultural sense. Minnesota fits most definitions of midwest, but culturally it also aligns more with the eastern Dakotas than, say, Ohio. The Dakotas don't fit the geography of the midwest term, but whatever. The Dakotas and Minnesota have more in common than the Dakotas and Montana. There's ~1k miles between Missoula and Fargo with almost nobody between them. Culturally there's very little connection aside from the border region, which is largely unpopulated.
The Dakotas and Montana both contain the Great Plains, but the flatlands of Montana are, well, badlands. Traveling west from the Dakotas, there isn't a population center in Montana until Billings, which is midway through the state and quite mountainous. Missoula and especially Bozeman are deep in the Rockies. Missoulians tends to see themselves as part of the Pacific Northwest and Bozemanites as part of the Rockies, fwiw.