Despite the protestations of some people who become famous in a particular genre of music, there are famous musicians in every genre who played in different bands in different styles while they were “paying their dues”, and the only reason they’re known for a particular genre is that they just happened to be playing in that particular genre when they got noticed.
There are plenty of country singers who played in rock bands when they were coming up - Garth Brooks is a well-known example. I’m pretty sure Rascal Flatts was a pop rock band that wasn’t going anywhere until they “countrified” their sound. And it works the other direction as well. Marilyn Manson’s guitarist, John <some number I can’t remember here> played with country singer Trisha Yearwood (IIRC) before joining Manson. There are thousands of unsigned bands out there that change their style to match whatever the “current thing” is, hoping to get noticed by a record company. Kevin DuBrow of Quiet Riot once stated that most of the L.A. “heavy metal” bands that hit it big in the '80s were playing power pop a few years earlier.
What it boils down to is musicians who love music and want to perform music for a living. They’ll do what they have to do. Very few of them, if offered a spot in a band that had just signed a record deal, would say, “No thanks, I don’t play that style.” They’d learn to play that style.
Then there’s the simple fact that the odds of getting a “rock” record deal past the age of 30 is pretty low. Rock is marketed mostly to teens and 20-somethings, so record companies are looking for acts that can project a youthful image. Country and some other genres are more open to older artists, so it’s natural that an aging rock singer might gravitate toward country.
ETA: Eric Adams, lead vocalist of “true metal” band Manowar, performs in Broadway musicals when Manowar isn’t touring or recording.