Got a PM requesting that I look at this.

List matches with the verb has - both singular.
Animals matches with the verb exhibit - both plural.

Here's the structure of the sentence:
The list - of animals - that exhibit X - has been expanded to include Y
Main subj - prep phrase - "that" modifier, modifying the preceding noun, animals - main verb (plus the rest of the sentence)

Read it as:
The list (of animals that exhibit X) has been expanded (to include Y).

You can also use logic to help you out a little. Are the animals exhibiting X or is the list exhibiting X? X is a characteristic of animals, not of a list - a list can't exhibit a preference for left or right-handedness.