Whether you're a Satanist, a Kali devotee or a Setian, there's always that fact of having to worship (or relate to) some deity that is of a very different culture. In every path I was in, I found myself always with the same problem. I feel at home with the Celtic things, but I have to concentrate, study and follow a god or goddess that belongs to a totally different culture than the one I like. How do you deal with it? BTW, Celtic gods never wanted to stay with me for long; maybe it's a matter of not having enough Celtic blood... who knows.
I dealt with it by taking the time to study and soak in everything. First for a few months just trying to grasp Trika, then I did some of my own exploration inside of myself as I wasn't ready fully yet (despite knowing it's what was probably right for me).
Then I spent a couple of years exploring more orthodox stuff, so getting a context from other schools. Then I started to return to Trika. I started to find that over time I picked up more. I was always bad with studying and reading so this process was slow for me. I've been a Hindu for about I wanna say 5 years? Been a Satanist for 7. What I'm doing works for me but I didn't become comfortable with it fully until maybe last year as my understanding of Trika took some leaps and deepened and it put to ease some of my anxieties about my blend.
My point is, maybe for you, its' a comfort thing. You want to be authentic, and understand it. Make sure you are on the right path.
But I got to where I am now by just always being willing to soak in new information on Hinduism; there wasn't some magical moment or insight that caused that. There is still a lot I don't know but I can have a conversation with most sects I'd encounter now. Sure, I had leaps of insight into the religion itself, but we experience that with any "aha!" moment of learning.
So really the answer is plain simple. Study, learn. Stick with it. There is no special answer that will make it easier. If it isn't your path, you will find out MUCH quicker this way too as along the way you will be able to figure that out.
And if you keep finding yourself drawn to something you disagree with, it could be because you know it's true, but are not emotionally able to accept it. I've felt this with Trika, abandoning some aspects of Satanism but funny enough as I matured down Trika those aspects of Satanism re-emerged with a more full understanding. The old understanding had to be abandoned so I could grow, and only then could I realize I was right before, just not in the ways I thought. I didn't re-embrace everything, but it was through this process I accepted what I was drawn to while not throwing the baby out with the bathwater. So don't be afraid to be in a state of uncertainty as you are learning. Not all pieces will fall together automatically or even for a good while. Be honest about this, least you fall into double think or contradict yourself. Holding two possibilities is different than holding two certainties.
Anyways enough of my rambling, I hope I said something of use here