I got 5 bucks that says the real reason is that they don't want their faithful watching women go into positions that can only mean one thing.
Why do you think the women pray behind the men? Watching an entire row of women do that bend over thing makes keeping your mind on matters of faith tough, real tough.
They don't advocate going to strip joints either.
I'm not saying strip joints and yoga are the same thing.

However the similarities are striking.