Nah, the jury's out on this one. I think most authorities are leaning towards allowing the split infinitive, if used properly, since it can often eliminate confusion in sentences.
Your sentence, "Linux users need to give up the animosity and save their hatred" is okay grammar IMO. Grammar should and tends to have a logical basis, not a pedantic one, and if the reader doesn't have to expend any more energy on understanding the sentence then it should be fine.
It's not a split infinitive; that was a joke that isn't all that funny anyways, but won't make any sense unless you actually know what a split infinitive is. "To boldly go where no one has gone before" is an example where the word 'boldly' splits the infinitve 'to go;' it's done exclusively for emphasis.
I tend to agree that grammar is focused on logic, but this is not purely academic. The reader for which Grammar is designed is the most naive fluent reader. In the above example, the split infinitive is poor grammar because it will trick a naive reader in to thinking the verb is 'to bodly;' an irrecoverable mistake. It's important to follow the rules when you're writing, because it's not a trivial operation for the reader to say "what did you mean by that?"
Grammatically, iago's sentence makes no sense without the second 'to,' as it changes the tense of the second phrase, after a rather confusing shuffle. To a native speaker, it's intuitively obvious what the intention was. Someone who is not a native speaker, even if they are fluent, is apt to read the sentence literally and become confused.
I write like I speak.
Actually, you write as you speak! 
Like works well in that situation, since he probably doesn't type exactly the same as he talks (I know I don't).
Wrong. It's a
simile. You can't put the word like there; its grammatically invalid.
