Vance hit on some excellent points, but for me... it's less about believability and more about it just not fitting in with the feel of Indiana.
Raised Christian and still very much a believer myself, I still have no issue at all watching and loving the heck out of ToD which has nothing to do with Christianity at all (except that Mola Ram wanted to "bring down the Christian God"). I have no issue watching and loving Star Trek/X-Files/Babylon 5/Star Wars, etc, etc... all with aliens out the wazoo. Aliens and Indiana Jones just don't feel right together. Like Gary Cherone fronting Van Halen... it's still Van Halen, but it doesn't feel like Van Halen.
And I think the alien angle would have been a bit more "Indy" if it was left to more mystical devices. More allusion, more mystery. Have things happen that don't flat out tell you and show you "look aliens" but have it more like "what the hell was that!? could that have been aliens?" Lucas (and just about everyone these days) feels the need to explain everything flat out, under estimating the intelligence and imagination of the viewer, gone is the allusion, the subtle hints, the ambiguity that left the view wondering... now we get a blatant flying saucer, a blatant "living alien". It's like the original Wampa scene in Empire vs. the SE Wampa scene. The original was cut and shot that is left you with glimpses, sounds, enough information to stir the imagination and form your own pictures and conclusions. It was still the Wampa, and it still beat the crap out of Luke... but we got to fill in the gaps about the power and terror of this giant snow beast, but then we get the SE version and it's very "this is a wampa, this is how it eats, this is how it walks, this is how it howls when it gets it's arm cut off, ok next scene". That's my take on it.