The Yoga practices of self-awareness, self-training, and self-discovery are non-sectarian, and are compatible with all religions. If you are familiar with the differences between Yoga and religion, it is easy to keep them separate, or if you prefer, to integrate them. The choice rests with each person as an individual.
1) Keep them separate: If you wish to keep Yoga, religion, and spiritual matters completely separate, this is easy to do. It simply means practicing and studying your Yoga at places, and with people who share those same values and orientations of Yoga not being part of religion. Each person is free to follow their own religion in their own way.
2) Retain and blend your religion: If you wish to practice Yoga, including its deeper, more authentic, spiritual aspects, retaining and blending the religion of your youth, family, and culture, that too can be done quite easily (keeping in mind, however, that authentic Yoga will lead one towards the esoteric or mystic and of the spectrum of religion).
3) Choose a new religion: If you wish to integrate Yoga with a religion new to you, and you are with a teacher or organization whose values and orientations match yours, this too may be done.
It seems most useful to have inner clarity about one's own religious preferences. Then it is easier to choose whether to practice Yoga separately from religion, in the context of religion, or with no religion at all. Then, the aspirant can attain all of the benefits of both their religion and of Yoga. The benefits of Yoga are for everyone.
All of these options are available to each of us in our practice of Yoga. There is a simple reason that these options are available. That is, Yoga truly is not a religion, and thus, Yoga can serve all people of all faiths or beliefs.