You have missed something very important from your quote:
Now, it is difficult, perhaps impossible, to bring forward one case of the hybrid offspring of two animals clearly distinct being themselves perfectly fertile.
The words "clearly distinct" appear, on the website you linked to, and in Darwin's text which appears in an image on the page, in italics. Italics can be used in place of quotation marks; they can also be considered to denote parenthetical text.
Consider it written this way:
Now, it is difficult, perhaps impossible, to bring forward one case of the hybrid offspring of two animals, clearly distinct, being themselves perfectly fertile.
Darwin is saying that it is impossible to give an example of a hybrid animal which fits two criteria:
- that its two parent animals are "clearly distinct" - different species from one another
- that the offspring itself "is fertile" - capable of sexual reproduction.
"Being themselves" in this context is perfectly idiomatic. It means that the hypothetical hybrid animal to which he refers exists in a particular state. In this case, that state means capable of reproduction. The use of the word themselves is to set them in contrast to the other two hypothetical animals which are tacitly referred to - the parents of the hybrid, which of course were capable of producing offspring.