How do Christians explain commonalities between their religion, other major faiths and obscure isolated tribal belief systems? Many belief systems share common themes; an afterlife, rebirth, bodily mutilation and sacrifice.

To me this suggests a shared origin either in history or storytelling (Abrahamic faiths) or that they were all "made up" to appease basic human fears or death and to cope with grief.

Taking these similarities into account how do Christians dismiss other beliefs and accept their own as the one true religion?
Occam's Razor states that the simplest solution is likely to be the correct one, and such commonalities are generally explained by Christians by appealing to the simplest solution: when two separate entities share several common traits, it's generally because they derive from a shared origin.

The Old Testament gives a few tantalizing glimpses of things that make a lot more sense in the context of Christianity, especially in the account of events that predate the Law of Moses, but the record is rather sketchy, and mostly limited in scope to the people of Israel and their predecessors.  But from extrabliblical historical and religious works of similar antiquity we get a picture of the rest of the world, and of striking similarities in the details of their worship customs, and the further back you go, the more things converge.

To give just one example, we typically think of ancient Greece as the birthplace of Western thought, but religiously they were anything but!  If you were to mention to an ancient Israelite the notion of a God of thunder and lightning and fertility, who is the leader of the pantheon and lives on top of a mystical mountain, he would immediately recognize the concept: you're talking about Baal, the chief god of the Caananites!  (And in fact Zeus's consort's name is only one syllable different from Baal's Asherah.)

Now the name Baal is a Hebraicized version of the Babylonian Bel, and Babylon was built at the site of Babel, where humanity was once gathered together before dispersing from that point.  (There's been some very interesting research into ancient Babylonian history that identifies the legendary Tower of Babel with the Ziggurat of Babylon, for example.)  And one of the high points of Baal's legend was a resurrection tale involving him being murdered by his enemies and coming back to life a few days later, imagery that should be immediately familiar to any Christian.  Where did this notion come from?  From when a good portion (all?) of humanity, including true worshipers of the Lord, lived in and around the land of Babel, of course.

These sorts of convergences show up all over the place when you start looking at the details of ancient religious systems, and they only really make sense if you assume a common origin.