They're/There are the men you are looking for.

1. They're (= They are) the men you are looking for.
2. There are the men you are looking for.
(my bold, Essays on English Grammar and Rhetoric From Traditional to Modern, by Ting-chi Tang, page 186)
According to the author, the above sentences have phonological ambiguity, which means they have the same pronunciation but different meanings.
Do native speakers agree with what he says?

No, they and there are pronounced differently and mean different things. The difference in pronunciation is probably less distinct if it comes from non-native speakers.

About 99% of native speakers don't know what "phonological ambiguity" is, and I'm not sure myself. They are not pronounced the same, but the pronunciation is similar. They do mean different things. However, there is not likely to be any confusion. There is always context for everything.

The two things could mean the same thing. Suppose you are pointing at a group of men. If you say "They are the men you are looking for" you are effectively saying the same thing as, "There are the men you are looking for."

(I can't imagine using "They're" in the first sentence, but in any case my answer is the same.)

No, he's got that quite wrong. These two are the same:

They're
There

Therefore, the second sentence has a crucial extra syllable—a schwa for the word are.