Chanting is often associated with religion and has been used by all forms of religions throughout history from Buddhism to Christianity. I think that this is one of reasons why some people feel uncomfortable chanting in a yoga class, as well as feeling self-conscious at first. Many chants, especially Kirtan chants, are devotional and this, once again, can cause some questions to arise.
From personal experience, chanting can have a very positive, uplifting effect on you, irrespective of your religious beliefs. It allows the mind to be free of any other thoughts that may be distracting or disturbing you. Chanting with others can also bring about a feeling of belonging and energy is shared. When we chant, it is said that we cut through the mind mesh and obtain freedom from delusion.
I have included some quotes below which I like a lot and which can be interpreted in many ways. I find them very useful for quietening the mind and feeling good about oneself.