"Western wear" as we know it is mainly a post-World War Two creation of the Country & Western music industry and the rodeos. Some stockmen still largely ignore the look. The Old West did not have it.
But in Austria . . . Austria! . . . it can be ecclesiastical. Sort of. Some Roman Catholic observers are very upset. They seem equally bothered by the Confederate battle flag as by the cigarettes. (Would "Yeehaw!" be considered a "pious ejaculation"?)
I don't exactly have a dog in that fight. I just did not know that the concept of "cowboy church," not uncommon around here, had been exported — and had swum the Tiber to boot.