The eff word IS popular in Montana, though not in front of the womenfolk... Just like about everywhere I've been.
But I have never been able to stomach Yellowstone. It's just soap opera bullcrap wrapped up in boots and belt-buckles. It ain't Cowboy way, not anything like it.
I'm not unfamiliar with the use of the word. I had an old friend who died recently who used it in many forms. One time I bet him that if he could not use it for a month, I'd buy him a steak dinner. He couldn't do that.
Then it was one week. He couldn't do that.
Then it was one day. Nope.
I have other friends and family members who would use the word occasionally but not in as many varieties and permutations as my late friend. But even he would (mostly) never say it around females.
For the most part here in Wisconsin, you will not hear the word in polite conversation. But you will hear it.
I had heard that the Irish are very fond of the word. But when traveling through Ireland for three weeks some years ago, the wife and I scarcely heard it. Maybe the Irish don't swear in front of foo*in' foreigners.
I get the feeling Hollyweird scriptwriters think everybody in America, even small children, use the word profligately. I don't think Americans of whatever class rank use it nearly as much as the scriptwriters think we do.
At any rate, the overuse of the word really takes away from the show.
And you're right overall....it's too much overacting bullcrap. Way too many plot devices that defy belief other than the ridiculous swearing. Like cowboys can't leave the Yellowstone ranch as if they're in the Mafia or something. Like branding somebody couldn't cause a huge infection problem.
I don't know how it got such great ratings. I have to suspend too much disbelief.