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Is there any common consensus among Christian denominations about what constitutes law (as applies to Christians) in the post-Christ era?
Your research is accurate; Roman Catholics and Protestants (adherents of Sola Gratia, specifically) fundamentally disagree on this subject. If you're asking specifically about whether Christians agree on what is necessary for salvation, then the answer is a resounding "no". Accordingly, I suspect you're going to find disagreement as well whether the law still "applies", although you'd also have to go further and clarify what you mean by "applies".
For example, one analogy I've encountered from the Sola Gratia camp goes something like this. You die. You stand before God in judgment (sort of like a court room). You are found guilty under the law. Before sentence is passed, however, Christ steps in front of the judge (God the Father) and asks for mercy on your behalf. The judge agrees and commutes your sentence.
That said, this is getting into complicated waters, for which a brief answer can only really scratch the surface. You might also want to ask for the perspective of a particular denomination, at least to the level of e.g. Orthodox, Roman Catholic, Anglican, Lutheran, Calvinist or Armenian. (I might be forgetting some, and the last two especially can be broken down into additional, finer gradations.)