Corresponding noun for "side-effect-free"?
A good rule of thumb for grammatical questions is, if it's so complicated that you need to ask, it's better to just rephrase the sentence.  For example, "Side-effect-freedom of the function guarantees X" is more simply and elegantly written, "Because the function is side-effect free, X is guaranteed" or even, "The function has no side-effects, so X is guaranteed."

Having said that, keywords for articles are expected to be noun phrases so that would be a place to use "side-effect freedom".

(By the way, "non-side-effective" is an adjective.)