In the song, you're right that it's wrong. It should say, "What if God were one of us?" That's because the rest of the song is in the present tense and because the frequent use of the conditional mood afterwards isn't ever placed in the past.
It would only be correct if talking about the past, i.e., the past tense version of the question "What if God is one of us?" But if positing a hypothetical, or "irrealis," that has no timeframe because it isn't real, meaning it hasn't happened, isn't happening, and will probably never happen, then it should be "were" because it calls for the verb to be conjugated using the subjective mood. Particularly on that last point, if it's something that you wish to express will probably never be, then that's when you use an irrealis rather than the present tense, which you use when you want to toss those doubts aside, even if only for the sake of argument or hyperbole, like using the question to affirmatively suggest that God actually is one of us.
* What if God were one of us here right now?
* What if God was one of us at the movies yesterday?
If God had a name, what would it be?
And would you call it to His face?
And yeah, yeah God is great
Yeah, yeah, God is good
Yeah, yeah, yeah, yeah, yeah
Since the first verse above says "would you call it to his face" instead of "would you have called it to his face, we know that "had" expresses the subjunctive mood rather than the past tense. Then in the second verse above, because she uses "is" instead of "was," she makes it abundantly clear that she's not talking about before but rather right now. That makes it reasonable to conclude that the "was" in the following verse should be "were" as it is expressing an irrealis:
What if God was one of us
Just a slob like one of us
Just a stranger on the bus
Trying to make His way home?
The reason this mistake happens so often is the conjugations for the subjective mood and for the preterit tense are identical for every verb in the English language except one: "be." "Be" is the only verb where some of the conjugations of the subjunctive mood are not identical to the preterit tense, specifically those for the first person and first person plural.
be - preterit tense
he, she, it was
you all were
be - subjunctive mood
he, she, it were
you all were
When you actually do want to express an irrealis that, while remaining out of time because it never happened, is nonetheless couched within a context of past events, then the pluperfect subjunctive mood is used, for example:
* If God had been one of us, who would he have been?