The phrase increasingly heard introducing utterances emanating from the mouths of American speakers of English (but not only), the reality is, typically followed by the reduplicative copula is + that––i. e., the reality is is that––can only be adjudged a hypertrophic way of saying what could easily be said more succinctly by using the word actually.
This particularly odious case of hypertrophy is of a piece with all such instances––especially of pleonasm proper––that are inundating American English. One could perhaps provide some weak justification by assessing it as a form of emphasis, where the substantive reality gives the phrase some modicum of substance missing from the adverb actually, but rarely is any emphasis intended by the speaker or demanded by the context. Stylistically, the reality is can be chalked up to the inbred prolixity of speakers used to passing off hyperurbanisms as if they were the coin of the realm instead of the counterfeit that they are.