The full answer

"That" is consistently capitalized in all title case style guides. Whether it functions as a demonstrative pronoun, a determiner, or a subordinating conjunction, AP Style, Chicago Style, MLA Style, NYT Style, and AMA Style all capitalize it.

Unlike coordinating conjunctions such as "and," "but," and "or," the word "that" when used as a conjunction is a subordinating conjunction. Style guides that lowercase coordinating conjunctions do not extend that rule to subordinating conjunctions like "that," "which," and "because."

The four-letter length of "that" puts it at the same length as "with" and "from," both of which are lowercased in Chicago Style as prepositions. The difference is that "that" is a pronoun or conjunction, not a preposition, so it is capitalized.

APA Style, Wikipedia Style, and Sentence Case lowercase "that" in the middle of a title because those styles do not make grammatical distinctions — only the first word and proper nouns are capitalized.

"That" can function as a demonstrative pronoun pointing to something specific, a determiner modifying a noun, or a subordinating conjunction introducing a dependent clause. In all three roles, it is capitalized in title case.