Perhaps this isn't what you're looking for, but Martin Scorsese's Silence is excellent for me. It's not a secular movie with hints about Christianity, it's clearly a movie about Catholic priests going on a mission. But it's the exact opposite what you think movies like this are - it's not about preaching or hammering some "correct" doctrine into your face, and if one goes in looking for that experience they're going to be in shock. It's more about dissecting and even destroying religion in the face of suffering and harrowing doubt until there is nothing left except...well I won't spoil it any further. But I sincerely recommend it. Hard watch, but worth it, at least for me. One of my favorite movies ever made, and there's some brutal honesty about it that I admire. I don't think that movie has a hidden agenda, it's not sneaky.
Also Bringing Out the Dead from the same director. Some of it's not subtle, some of it goes by without you ever noticing it. I didn't notice much of it myself until much later.
About music, Sufjan Stevens. A true musician. He's only made one clearly Christian album, but even that is honest and genuine, not preachy or trying to get some message through in a superficial way. Iron&Wine as well, a lot of Biblical imagery, alhtough he's not religious I think, somewhat critical of it at times. And good old Nick Cave, can't forget about him.