It is fairly common to run up against students who are afraid of the big Y yoga. That is, the yoga which encompasses several tools designed to advance toward Self-Realization. For example: chanting (Mantra yoga), meditation (Laya yoga) or praying (Bhakti yoga) can and should be part of a well-rounded yoga practice. But this freaks a lot of students out. To them, chanting Om is something New-Age or against their religion.
The practice of yoga is an ancient science. The idea is to clear away all the muck and grime that we accumulate by being humans and get acquainted with our true nature. The Indian yogis, those who obtained enlightenment, did so through devotion to god. And to that matter, one doesn't even have to believe in god to be on the yoga path! There's a path for athiests (Jnana yoga) which focuses on knowledge and intellectuality.
The Hatha path, which is the practice of asana as done in a yoga class, is considered the most difficult and forceful of all of the options. I am currently on page 147 of Autobiography of a Yogi by Paramahansa Yogananda and he has yet to do a single yoga pose. His path to the Self was one of meditation and devotion to god.
So the next time your yoga teacher invites you to chant Om with the class, consider it! You can use it as an opportunity to ponder why you are in a yoga class at all. If you were simply interested in working out, wouldn't you just go to the gym and run on the treadmill? In my opinion, there is a reason that we're drawn to the practice of yoga and it is part of our path to figure it out.
And if you experience fear as a result, try to open your heart to the antidote to fear, which is love.