I hated the one Yoga class I took; too slow, boring music and the woman droned on and on about meditation as a gateway to the Soul. I'm a religious person and I was uncomfortable with her history lesson on the monks using Yoga as a form of worship.
I totally understand where you're coming from. There are several styles of yoga (Ashtanga, Bikram, Iyengar, Kundalini, Viniyasa, just to name a few), not to mention individual variation among instructors. When I teach group practice, I try to make my classes inclusive, so I focus on what I feel is the biggest benefits of yoga for EVERYONE; namely the physical poses (asanas) and the breathing techniques (pranayama). Although I do know Sanskrit, the chants, and about the other spiritual aspects of yoga (which are based on the Hindu religion), I do tend to steer away from them because of the alienating effect it can have on people of other faiths. The chants and some of the traditional sequencing of poses really ARE devotional practices to Hindu deities, and if anyone tells you otherwise, they are either misinformed or being ingenuine. But if we focus on the asanas and the breath and sequence and modify based on the individual body, then everyone gets what they need from class. And yoga can be more intense (power yoga = Ashtanga), make you sweaty ("hot yoga" = Bikram), or be more restorative. The key is finding the right practice and the right instructor for you.
Pilates too has a couple of different styles, most notable the "traditional" style of Joseph Pilates and the more putatively "modern" approaches (Winsor, Stott) which advocate modifying the traditional mat and equipment approaches based on their interpretations of exercise science. Again, your pilates experience is going to be largely influenced by the skills of the instructor, too.