I do not, for the life of me, see how a person can hold two really opposing beliefs at the very same time.
You can't; there's no doubt.
However, I'm going to use that as a springboard for a brainfart and mini essay to the general public, so don't take it as directed at you.
Not every religion is monolithic and diametrically opposed to others. There are schools of Buddhism that have more in common with Hinduism than they have with other Buddhist schools, and believe it or not are even compatible with Hinduism. It's a misconception that all of Buddhism rejects the idea of atman for example; Shentong does not reject it. Sufism probably has more compatibility with Buddhism and Hinduism (the schools of Buddhism and Hinduism that are compatible, that is) than it has with mainstream Islam. And the gnostic and mystic sects of Christianity have more in common and compatibility with the eastern religions than they do with mainstream Christianity.
We humans love our labels and tend to compartmentalize things. But I think religion is a spectrum or continuum rather than a "It's This or It's That" with nothing in between. It's not unlike language. Moving westward from Germany to the Netherlands, where does German end and Dutch begin? Where does Hindi end and Gujarati begin? There's a continuum of dialects in between that are compatible (mutually intelligible) until you finally do get to a point where they're not mutually intelligible. For religions that would be the incompatibility and complete opposition. But somewhere along the continuum there is compatibility. This is where people like me fit in and can make it work. Not everyone can or should try. Why does this happen?
That's what makes horse races, they say.