Iguanas have been an important food source

In this sentence, "they" is correctly referring to animals. We can use both "they" and "them" to refer to plural animals.

You're right to be suspicious of pronouns when it comes to animals, though, since we would not use pronouns such as "who" and "whom" to refer to animals.

Here's an Official question that correctly uses "them" to refer to animals:

For the farmer who takes care to keep them cool, providing them with high-energy feed, and milking them regularly, Holstein cows are producing an average of 2,275 gallons of milk each per year.

(A) providing them with high-energy feed, and milking them regularly, Holstein cows are producing
(B) providing them with high-energy feed, and milked regularly, the Holstein cow produces
(C) provided with high-energy feed, and milking them regularly, Holstein cows are producing
(D) provided with high-energy feed, and milked regularly, the Holstein cow produces
(E) provided with high-energy feed, and milked regularly, Holstein cows will produce