This is a question that everyone who begins a yoga practice (for whatever reason) must eventually face. The simple answer is yes, but not necessarily in the way you might think.
There is no question that yoga began as a very specific kind of spiritual practice. The history of yoga makes that very clear.
The thing is, though, that up until incredibly recently yoga was a practice that rested on the fringe of society, practiced by weirdos or, worse, the boogeyman (yep, in many parts of India the yogi is a scary, monstrous, not-quite-human type creature who is at best a trickster and at worst totally evil). This means that over time the spiritual practice of yoga has changed dramatically. The goal was always enlightenment (unless you were the boogeyman), but the specifics of what that meant and how to achieve it shifted with the times, either to complement or differentiate from the religious practices of the day.
The most recent transmutations of yoga’s spiritual philosophies are much broader than they used to be, perhaps because it has come into contact with a wider variety of cultures and religions. Instead of prescribing a single method for obtaining a specific kind of enlightenment, it prescribes a few methods for obtaining whatever kind of enlightenment you fancy. An easy image is that of a ladder that can be set up alongside your religious or spiritual practice of choice. It helps you get in touch with your true self and connect to your Source as conventionally religious, atheistic, or new agey spiritual as it may be.
So while we often think of some specific religions when we think of yoga’s spirituality, the truth of the matter is that it’s more than that. Or maybe less. It’s a tool that you can use for your own spirituality, however you define it.
The story doesn’t end there, however, because since a physical practice was added to yoga’s repertoire, it can be even simpler: a practice of physical fitness, allowing yogis to stamp almost all of the spirituality out of yoga. Unfortunately, you won’t get off that easy – to get the full physical benefit of yoga it requires a level of self-awareness that doesn’t exist in other forms of exercise, and if you ask me, getting in touch with yourself means getting in touch with something deeper, no matter how you want to name it.
So at the end of the day, yes, yoga is a spiritual practice. But now you get to define what that means for you, and I think that’s pretty cool.