It's not just Bozeman; it's the entire West. I grew up in CO and have lived in AZ, NM, OR, CA, MT, WY... folks were complaining about the CA influx in CO since the 80s (maybe before)... And it's real. Cash out, find a cool town, move to it. I could add that many then expect their newfound home to be like wherever they came from, and this is the kind of action that leads to post like the one that started this thread. We left the West (Oregon) 3 years ago in large part because it had changed so much and we didn't have 1/2 million for a modest house. My folks sold their house they'd had for decades in Bozeman about two years ago, in a day... To a Simms exec. The Bozeman they loved was/is gone. It is a new place now, loved by the crowd so well described In the OP.
And, who can blame folks for wanting to experience these places?; the American West is gorgeous. Every outdoorsy catalog, magazine, website, blog, you name it is full of photos of beautiful places all over the West. Everything is Epic. Any young person with an interest in the outdoors is sold The West and many move there to experience it. Many have dreamed about moving there for their entire careers and finally make it happen when they retire.
It's heartbreaking to lose a place you love, but that's part of today's America.
We're now in my family's 1800s farmstead in our rural, one-stoplight cow county full of hillbillies and rednecks (there's a difference) and there is still a mild hipster influx. But at least we can afford to live here for the time being.
My inlaws retired last year and bought a converted sprinter... I don't think it's very fun to drive.