In my opinion, writing it out lends a bit more formality to it. Also, Jew on it's own (again, just me) has been an easy, short jab of an insult for millennia.
"As a Russian person, I can say that we don't have such a difference in our language, so it's new to me". Compare: "As a Russian, I can say that we don't have such a difference in our language, so it's new to me". It's true: that adds formality to it. To be frank, it's possible to translate "Ecksian person" into Russian proper: "человек иксовой крови" or "человек иксового происхождения", but it sounds more anthropological.
Perhaps my phrasing was wrong, then. The way it was structured in my brain was how Jew has become an insult or pointed quip over millennia; thus, writing the long form of identification makes this more personable. The two points aren't mutually exclusive. The statement is who he is, and being very clear as to not mix in the stigma of what a "Jew" is.