Interesting question. Now that we know that the Salvation of Jews does not depend on faith in the Second Person of the Most Holy Trinity, we can dare to ask the question: 'Can a Catholic be righteous in the Sight of God?' I look forward to the next Pontifical Commission for Religious Relations with the Jews document to fill us in.
Apparently, according to at least one Jewish sect - and a powerful one at that - Chabad Lubavitch, the answer is yes, which for us Catholics - though we are known only as Gentiles, will come as a great relief. Apparently, you can be righteous in God's sight, as long as you follow the Noahide Laws, as one Italian Catholic, who enquired to the organisation about becoming a Jew, discovered.
Of course, some 'rigid', 'fundamentalist' types might believe there may be some conflict between being 'righteous' by following the Noahide Laws and proclaiming faith in the Saviour of all mankind, Our Lord Jesus Christ, because a proportion of Jews (it's so unfair to treat them en masse as a block, don't you think?) may well regard faith in Jesus Christ as somewhat idolatrous or blasphemous, but the Pontifical Commission will, I am sure, fill us in on the details and we'll cross that bridge when we come to it. These are just petty details that can be ironed out later on when we are all 'united'.
I'm sure that Our Blessed Lord - and St Paul - had much to say on these matters, but we've moved on now and we're not so 'self-enclosed' as we once were. I'll let Rabbi Aaron L. Raskin fill you in for the next two or three hours on how you, as a Gentile, as a Catholic indeed, can be made righteous in God's sight, here, here and here.
After all, if the Catholic Faith - if Faith in the the only Begotten Son of the Eternal Father is no longer necessary for Jews to attain Salvation, there's no reason faith in the only Begotten Son of the Eternal Father is necessary for Gentiles either - even Catholics. So let's all just be righteous together and be righteous dudes and dudesses. Then, at last, we will be united and the world will have peace. Quite why the Church is telling Jews they can have Eternal Life without the Divine Faith of Christ is a mystery in itself, because Jews don't seem to believe in Eternal Life nor in the Man Who promises it to those who are faithful to Him. Why does the Vatican want to tell Jews they can have something they don't even believe in or even want? Jews don't believe in Salvation in the sense in which Jesus taught it, if at all. The question is: Do we?