And don't forget the similarities between Jesus' and Littlefoot's birth.

But seriously, there are two other possibilities as well:
a) the movie-makers touched upon Christian concepts while being unaware of touching upon them, or
b) merely used tropes that were introduced into animation by Walt Disney, who himself might have touched upon Christian themes knowingly or unknowingly (by some things I read before, it was very much knowingly, but I can't remember the source so this might be speculation)
Our culture shapes the way in which we think, even if we are unaware of it or openly deny it. For example, when Auguste Comte, the founder of positivism, wanted to replace Christianity with the "religion of humanity", he went so far as to introduce three pillars of religion (Altruism, Order, Progress), seven sacraments, hymns, prayers, and even a calendar. It was essentially Christianity without God or Christ. Or take Friedrich Engels and communism, with its "fall of humanity" (the end of primitive communism of first human societies), its martyrs (fallen revolutionaries), its saints (personality cults of various communist leaders), and the achievement of true communism (the Thousand Year Kingdom after the second coming of Christ). Even some contemporary atheists, like Ray Kurzweil, can be included in this category, with their view of history as unstoppable nad unconditional technological progress that will end in the Technological Singularity, where AI moves so beyond human intelligence that the world becomes unrecognizable to human beings. Yet any of these people would be deeply offended if you called them Christian copycats, but that's what they essentially were.
So, I wouldn't completely exclude any Christian influence on Bluth and co.