CrossFit used to be a ragtag group of fitness rebels doing pull-ups in warehouse corners. Its adherents sneered at established health clubs with their acres of treadmills, scornfully labeling them “globo gyms.” Years of explosive growth have made CrossFit more popular than many of those traditional clubs.

The 15-year-old strength-and-conditioning program is so big, in fact, that many fitness clubs are creating programs that mimic CrossFit—from its moves to its gritty surroundings. CrossFit is drawing admirers at the very gyms...