I live in Whitefish and have Verizon. Can't say about other companies.
You get away from towns or major travel corridores...like US93, some of US2, (and not even then in some places)etc.....
don't count on your cell phone working.
I can drive 10 mins from my place in downtown WF and lose cell coverage.
Could be my older phone a 4 year old LG flip phone...but I would say coverage in the park is "spotty" for me. Places in and around West Glacier my phone will work, or sometimes not....inconsistent. I tried mine one day just after Haystack on the Highline....and it worked....for one call. I've heard some say if you get up high enough(in the park) to see a cell tower on one side or the other,,,,your phone might work.
I would never count on a cell phone working anywhere in the backcountry, especially at lower elevations, maybe mountain tops. I dunno. Never been on one in the park.