I mentioned to my sister that I was frustrated by my lack of access to yoga and she said that a priest at her parish gave a whole homily about how yoga is problematic and indeed prohibited for Catholics.
I was familiar with a prohibition against Eastern mystic meditation, obviously. My sister clarified that her priest said that the motions themselves are dangerous because they pay homage to dieties in whom we do not believe.
There is no way -- no logical way -- to make the case that the position of your body, bending and stretching into child's pose or downward-facing dog, is anything but morally neutral (not that there's no way to put your body into a morally questionable position, but that's another conversation).
Chanting "om" and clearing your mind, or meditating on your oneness with the universe, on the other hand: not morally neutral. Seeking Hindu enlightenment is self-evidently not Catholic. Don't do those things.
Intention matters and as always, one must know oneself. Are you the type to get caught up and lose yourself, to the point where you might find yourself chanting in an unknown language and emptying your mind in a quest for enlightenment? Danger, Will Robinson. If you are sure that you can treat it as pure exercise, and ignore all the mysticism, then go for it. We are called to be good stewards of our bodies and our souls.
For myself, I expect to have no difficulty whatsoever ignoring any calls to engage in mysticism. I'm going to be too busy either berating myself for wasting my time or rueing the day I chose to exercise at all, depending on the difficulty level. But I will be on the lookout for danger signs, because I just found out that I can take yoga at the community center in our neighborhood.