I am half Jewish and half Catholic. It sounds kinda confusing; how can you be half one religion and half another? It's not like we're talking about race. But that's the way I was raised and that's how I identify.
For a long time, that wasn't an issue, and it still isn't. But as I've gotten older, certain individuals have decided that this simply cannot be. The logic I am met with occasionally these days is that if I'm both, they cancel each other out and I'm neither. More often, some say that because my father is the Jewish parent (and not my mother), I am not Jewish, because Judaism usually says that the children take the faith of the mother. I think that this, in a word, is bullshit.
And here's why! Religion, unlike race, sex, gender identity, and sexual orientation, is a choice. Meaning, I could feasibly practice any faith that made me happy. Hell, I could be a Muslim if I decided it was good for me, regardless of parentage. So what does it matter if I say I practice two?
Orthodox Jews don't perceive reform Jews as even being Jewish at all, yet they're still Jewish. They each practice the religion in the ways they see fit, even though it's the same religion. Same here.
I don't blame anyone for being confused by the concept. It's definitely paradoxical, especially if you have no prior experience to it. My best advice (to myself and anyone else) is just to not think too hard about it. Religions change all the time. They're flexible. As it stands, many are only religious when it is convenient to them. Therefore, if we only listen to select rules, there really are no rules.