I think we need some perspective about what 98% of the DNA means. We share about 80% DNA with rodents. All animals, and especially all mammals share a similar basic DNA. The 98% makes us quite similar to chimps, enough to make it clear that we're a relatively recent split off (about 10 million years IIRC), but not quite as similar as the number suggests.
I really don't think this "elevation" was a result of religion because there is was no awareness that we were even related to apes until the 19th century. Various religions then of course denied this because it conflicts with their creation myths. I think that prior to the theory of evolution it didn't occur to anyone because the distinctions are rather obvious, one being that we can talk and write.
So we're related to apes, yes, but not apes. It's just semantics, really. We created all these classifications ourselves.
Definition of ape
1a: any of various large tailless semi-erect primates of Africa and southeastern Asia (such as the chimpanzee, gorilla, orangutan, or gibbon)
Find me a definition of "ape" which includes humans and I'll rethink it.