At a time when workout gear is fashionable, companies that make and sell sportswear are facing a strange predicament: their gear is too sporty for some.

Karyn Riale, chief buyer for high-end gym chain Equinox, has stopped carrying traditional brands such as Adidas at the shops in its locations. Instead, Ms. Riale said she prefers to make room for what she calls lifestyle brands like Michi, which makes mesh-paneled leggings called “Psyloque” and “Suprastelle.”

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