Grammaticality of “all things are become new”
It's archaic, but it was entirely grammatical when it was written.
Some English verbs used to be conjugated with "to be" rather like French verbs of motion still are. Modern English would use "have become". This also applies to "are passed away" in your quote.
Because it's archaic, it's occasionally still used now, particularly in Church liturgies, which tend to ossify language.
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