Definitely Calvinists are not Roman Catholics. That is something I think they are proud about. I suggest they are not even catholics (note that Romanism started 600AD roughly, all Christians before that were catholics - universal), and I suggest that is not something to be proud about. In fact that is something one should worry about (if one is a Calvinist).
Let me explain.
Well, if we take a typical Calvinist, we assume he would subscribe to the T.U.L.I.P. principle and would be an adamant promoter of Limited Atonement(LA). Here is the problem - the Nicene Creed.
Now I know Reformed people claim to subscribe to the Nicene Creed, but they do not really know what that implies. I find this specially true for Baptistic Calvinists. As typical I have found them to put their own spin on what the Nicene Creed. Case in point, the Nicene Fathers were not re-baptizers - remember the line " we believe in ONE baptism, for the forgiveness of sin"? A Baptistic Calvinists can not affirm that, since if you were baptized as a baby, you will be re-baptized by them once more, so right there Calvinists of Baptistic bent are out of catholicism.
Yet there is more and so I come now to their affirmation of LA. In the Nicene Creed we have one line which Lutherans affirm - on Jesus we confess - "who for us men, and for our salvation, came down from heaven, and was incarnate by the Holy Spirit of the Virgin Mary, and was made man;"
The phrase "who for us men" - means all of humanity that was how the Nicenes understood that phrase, so if you believe in LA, you can not affirm the Nicene Creed - for LA says that Jesus did not die for the whole human race, he only died for the elect - which is of course only a subset of the human race.
One has to really warp this passage of the Nicene Creed if confession to it and affirmation of LA is to be maintained. The two are incompatible.
So a question , if Jesus did not die for the whole world - that means he did not die for all men, then what happened in the incarnation? That is, we can ask this question - when Jesus became man, did Jesus leave behind the humanity of the non-elect - since after all according to LA, he was not meant to die for them anyway so did Jesus assume the humanity of these people whom he would not die for in the first place? No Calvinists I have asked dared answer this question, all I hear are just evasions. Clearly in the Scripture it says - he tasted death for every man - Heb 2:9.
Calvinists and UOJ are alike - and here is their fallacy - they conflate the Atonement with Justification. They both think that when one is Atoned for, one is automatically Justified as well.
As far as I know, only Lutherans who believe in Justification By Faith Alone, are the ones who make this distinction between Atonement and Justification properly and mediated by the Means of Grace.