Although I can't think of a single thing Witnesses *should* find wrong with Pilates... I would bet my last dollar someone will find reason to be "stumbled" upon hearing that someone is doing it. Pilates is about controlling your breathing in conjunction with the excercizes in order to maximize your workout. I have a couple of DVDs I like to use at home and they don't have any meditation or spiritualism, but focus more on awareness of your breathing and posture etc. But because Pilates and Yoga are so closely related as far as postures and such... I could really see people assuming (without bothering to check) that they are the same thing.
Some people just look for reasons to be offended, especially so within the Witnesses.