Yes, its totally okay to talk to a girl casually at the gym. Just dont interrupt her while shes working out and dont follow her around or anything like that. However, you dont go up to her randomly and try to force a conversation. Its not going to work, and its kind of a creepy and rude thing to do.

Is it OK to approach a woman at the gym?

You can absolutely engage in respectful, non-creepy conversation with women at the gym. The problem lies with the totally unrespectful and fully creepy ways that some men approach women at the gym, and the assumptions behind these behaviors.