In the phrase:
He demonstrated that he was true
What word class does that belong to?
In general, which word classes can it belong to? For example, relative pronoun, determiner, ...
THX
It is a complementiser, or subordinator. You could call it a kind of conjunction if you like.
"That" can also be a demonstrative pronoun or determiner. It sometimes also appears to be a relative pronoun (similar to "which"), but there is a preferable analysis where it is a complementiser and there is a suppressed "which".
Edit: correct "adjective" to "determiner".
In the sentence below, the word that is a subordinator:
He demonstrated that he was true.
... in some grammars this is called a "subordinating conjunction" or a "complementizer".
The word that can also be a determinative:
In some grammars if the determinative that isn't followed by a noun, it is regarded as a pronoun:
It can also be an adverb:
Relative that
That is the dog that we saw yesterday.
That may be considered a relative pronoun by some grammars. However, a number of very important modern grammars, for example the Cambridge Grammar of the English Language regard the that which we see before relative clauses as the same that which we see in the Original Poster's example. In other words, they regard it as a subordinator in both cases.