No, it’s not necessary that “as” be paired with another “as” in English sentences. It all depends on the sense and on what part of speech it is performing in the sentence—and about this I’ll have much to say later.
At the moment, though, let me first answer your question regarding the two “as”-using sentences you presented. I must tell you offhand that both suffer from faulty grammar and syntax. The comparative in your first sentence, “Animism regards the spirit world as stronger than that of the humans,” is stated in clunky, unparallel terms; in particular, the noun phrase “the spirit world” cannot be validly compared in strength with “that of the humans.” The comparison should be on a one-on-one basis—“the world of spirits” vs. “the world of humans.” So the semantically correct construction of that first sentence of yours should be “Animism regards the world of spirits as stronger than the world of humans.” I would say though that it would be clearer and more elegant to construct that sentence as “Animism regards the spirit world as stronger than the human world.”
Your second sentence, “Animism regards the spirit world as stronger than as that of the humans,” is flat-out wrong grammatically, semantically, structurally, and syntactically. The craggy, double-“as” comparative of that sentence, “as stronger than as that of,” is truly out of this world and should stay there for good.
Let me now take this opportunity to discuss “as” as a many-splendored word that can assume the role of as many as four parts of speech—as adverb, conjunction, preposition, or pronoun—and then to pinpoint those instances when it needs to be paired off with another “as” to work properly.
The adverb “as.” As an adverb, “as” needs to be paired off with another “as” to make a comparative indicating the same degree or amount, as in “Her dreams are as high as the sky.” If the degree or amount isn’t the same and the reference to the comparison is implied or clear to the listener or reader, the comparative needs only one “as,” as in “The last session was twice as long.” When “as” is used as an adverb in the sense of “for instance,” it need not be paired with another “as,” as in “She was referring to English proficiency tests, as TOEFL or IELTS.” There’s also no need for another “as” when the adverb “as” is used in the sense of something being considered in a specified form or relation, as in “I would like to discuss Jose Rizal’s generation as distinguished from ours today.”
The conjunction “as.” As a conjunction, “as” needs to be paired off with another “as” when used as a correlative after an adjective or adverb modified by the adverbial “as,” as in “The man accused of killing his girlfriend was as meek as a lamb when he was sentenced to life imprisonment.” No pairing off with another “as” is needed when “as” is used as a conjunction in the sense of “in the way or manner that,” as in “The boss wants you to behave as we do”; in the sense of “while” or “when,” as in “He yawned as he got up from bed”; and in the sense of “for the reason that,” as in “The newly married couple couldn’t take an out-of-town summer vacation as they were perilously low on funds.”
The preposition “as.” As a preposition, “as” doesn’t need to be paired off with another “as” when used in the sense of “like,” as in “All voted as a jury”; and in the sense of “in the capacity, character, condition, or role of,” as in “The law student works as a security guard at night.”
The pronoun “as.” Finally, “as” as a pronoun doesn’t need to be paired off with another “as” when used in the sense of “that,” “who,” or “which” after the word “same” or “such,” as in “She works in the same call-center as my son”; and also when used in the sense of “a fact that,” as in “Fair or not, many opinion columnists in media think the principal accused in the pork-barrel scam are guilty, as is evident from their sock-it-to-them commentaries.”
I think this is about all we should know about the various uses of “as.”
