Goats (Capra hircus) have been domesticated for over 10,000 years. For some, they’re meat. For others, they’re milk producers. And for still others, they serve as adorable pets or petting zoo staples.

Goats on yoga mats are not two things you see every day. But to 24-year-old yoga instructor Sydney Frost, the seemingly odd combination makes perfect sense. “I’ve always been really connected to ...