I've answered that before, but I'm glad you asked because that's a fruitful question to ask.
First, go and read this:
http://www.vor.org/truth/1689/1689bc00.html Specifically 11, 13, and 14, and 16. It's easier to point you there than reproduce them here. These summarize the doctrines of justification, sanctification, saving faith, and good works and their role.
Salvation, in our theology is a bracket term for several things and context dependent. It can refer to: regeneration, justification, sanctification, glorification, or all 4 elements of salvation. Sometimes people confuse us with the antinomians, and this would come from your side when confusing the doctrine of perseverance of the saints with the antinomian doctrine of eternal security. These intersect, but they are not the same. We affirm the former, not the latter. This is why when you characterize my doctrine as antinominian, I deny it. No, we do not,for example, affirm that works have no role in salvation or that salvation is like a tattoo you get and never lose no matter what and all sorts of things I've read or heard stated over the years. That's antinomianism - that's eternal security. You find that in the works of people that espouse "free grace." A classic contrast would be, let's say, John MacArthur on "my" side of the theological divide and those of,
these folks. That's not perserverance of the saints. I'd point out that Reformed theology is usually accused of being a version of "salvation by works" by these folks, not antinomian, ironic when you consider the opposite accusation comes to us from Roman Catholics. (Usually, this is because they are conflating "salvation" with "justification" (the antinominan objection) or in the case of Catholics and others like yourself "Saved by grace alone by faith alone" to mean the whole shebang, not justification by faith alone. "Salvation by grace alone refers to the root or ground of salvation, and via faith alone refers to the instrument of justification, not the sole instrument of salvation. Justification is one element of salvation itself. In Reformed Theology, Sola Fide (justification by faith alone) is a species of Sola Gratia (the ground and means of our salvation) which is Christ Alone (the Mediator of our salvation and the One on whom/in whom the merits alone around found). Again, read the Confession as starting point for what I'm articulating. That's a good summary.
What we are referring to here in this discussion isn't salvation qua salvation by faith. Rather, we're referring to salvation qua
justification.
That should frame the discussion.
When referring to the doctrine "justification by faith"...Protestants are referring to:
1. The underwriting merits of the root of justification. In our theology, the merit is that of Christ alone (that is to say the sole and sufficient merits of Christ via the atonement and the application of the atonement via
2. The instrument of justification - faith, not works qua works and/or faith and works in tandem. For example, I've interacted with some Catholics, usually former Protestants, who have said to me: Christ's atonement covers our sins in the past up to conversion but then we work in tandem and build on those for those after. That's probably the worst of the views I've heard, but it's an obvious, easy example to compare. Roman Catholic theology is more complex on that, sometimes depending on the source material as well the person articulating it (it can be mighty hard to find the Magisterium, but I digress), but that's the general idea.
In Reformed theology (whether Presby or Baptist versions), the Holy Spirit by means of the Gospel, not baptism, regenerates, the result is faith in Christ, this becomes the instrument via which God declares a person "justified." This is because Christ actually redeemed that person. The Holy Spirit, when His timing is ready, does this, and God's providence oversees it to ensure it occurs. Sanctification will result, and that person will persevere from the end. He may stumble,even gravely and struggle, but he will not apostatize, and this is due to the preservation of the Holy Spirit. Put another way, there's a limit to what he can do. Pilgrim's Progress, by the way, is an excellent allegory of that whole process, if you've not read it. It was written by a Baptist.
Put another way, Protestant doctrine stands in contrast to the Roman Catholic doctrine of the treasury of merit which is composed of the merits of Christ, the saints/church, and your own congruent merit (stuff you do,like, for example, the sacraments). To some extent, unlike your own group's ideas about baptismal regeneration as the instrument of application (as opposed to faith alone), this is bound up with their idea that grace is a substance that is conveyed by water (baptism) and the elements of the Eucharist (to take two concrete examples). The treasury of merit also underwrites several other Roman Catholic doctrines including the Marian dogmas and prayers to the saints.
In CoC theology, to take an example more familiar to you, the instruments (plural) would be baptism and faith. The classic reply to from my side is the same as the question of Scripture: was Abraham justified by circumcision? No, he was justified by faith (Romans). One of the cardinal reasons we disaffirm baptismal
justification is that if true it would be functionally the same as circumcisional justification, the doctrine that Galatians explicitly denies. Some Protestants, namely Lutherans, affirm a form of baptismal regeneration, but that is indexed to faith in a way unlike your own. Since I'm not Lutheran, I won't go any further. For the record, I disagree with Presbyterians over their views on infant baptism - I just worship with them because they are closer and there are are only 2 Reformed Baptist churches near me, and one of those is 20 miles away. The PCA also doesn't require you to hold to their ideas on baptism to partake of the Lord's Supper or even be a member of their churches. Some Reformed Baptists are kinda funny about stuff like that.
Sorry that rabbit trail, anyhoo
The position that links justification to works (baptism or others at all) turns on two exegetical fallacies when reading James.
These are, as I've pointed out, and you were I hope just glossing over before when this has been pointed out:
SEMANTIC INCEST
This is where a disputant uses one Bible writer’s usage to interpret another Bible writer’s usage. For example, James’ use of “justification” is employed to reinterpret Paul’s usage—and thereby disprove sola fide (Ijustfication by faith alone).
Or Paul’s use of “sanctification” is employed to interpret the sense of the word in Heb 10:29—and thereby disprove perseverance or special redemption.
But this is a fallacious procedure unless the disputant can show, independent of the comparison, that both writers are using the same word the same way.
SEMANTIC INFLATION
The disputant will equate the mere occurrence of a word with a whole doctrine associated with the word.
For example, a Catholic will compare and contrast Paul’s doctrine of justification with James’ doctrine of justification. But the mere fact that James uses the word “justification” doesn’t mean that he even has a doctrine of justification. That would depend, not on the occurrence of the word, in isolation, but on a larger argument. Words and concepts are two different things.
In context, James is simply talking about the difference between an antinomian faith that says one thing and does another, (he opens the discussion, remember, with a talk on favoritism in the church) for example, a faith says "Love your neighbor as yourself" but does not, in fact, practice it. The comparison is between a deedless faith and a living fruitful faith, not about the grounds or instrument of justification in the confessional sense itself. That discussion is in Romans.
So, independent of the comparison, Paul and James are talking about two different things when they use the term "justify". James' discussion in general in James 2 is more like the position that Paul is articulating in Romans 6 and 7 than the framing he sets up in Romans 4 and 5. James also isn't using the term "justify" in the sense Paul is using it. Both exegetical fallacies are avoided. Justification by works, invoking James, would directly involve one or both of the exegetical fallacies above.