There are no Briggs-ites, no Janssen-ites, no Fosdick-ites, and no DeWulfites. When liberals are removed from the church, it is done so under the category of heresy. Having no ground to stand on, they are unable to produce movements. Error, like a parasite, cannot exist on its own, but requires a large church organization to feed off of. When the liberal Lutherans formed Seminex after being kicked out of the Missouri Synod, it did not last very long.
There are, on the other hand, Machen-ites (the Orthodox Presbyterian Church, and the Bible Presbyterian Church) and Hoeksema-ites (the Protestant Reformed Church). When conservatives are removed from the church it is done so not on the charge of heresy but on “insubordination.” This was the claim against Machen, and McIntire, and Buswell, Hoeksema and Ophoff. But they were able to continue on with new church organizations, because they had not been kicked out of the true church, but the false. They, like Luther, are heroes of the faith. Luther himself, is perhaps the great first example of the Reformation; wanting to reform the church from within he did not leave of his own accord but was excommunicated for preaching truth.
In each case, whether Machen, Hoeksema, or Luther, they sought to obey God, not man. When the church becomes ruled in unbiblical ways, whether by Popes or Classis domination or by Boards, the true ministers will be pressured to conform. Insubordination is the cry. But it is a virtuous insubordination against the errors of man.
There have been many modernists, though there is no church of Charles Briggs. He only left a cancer in the PCUSA which has now consumed the denomination. Ralph Janssen’s higher criticism likewise produced no new denomination but left a cancer in the CRC. The impact of Harry Emerson Fosdick may be linked with Briggs. And the theology of Herbert DeWulf aligned with the increasing liberal CRC.
The test of Gamaliel has in time proven those who preach the truth. “For if this plan or this undertaking is of man, it will fail; but if it is of God, you will not be able to overthrow them. You might even be found opposing God.” (Acts 5:38-39)
Sorry Doug, but I think Frame’s term “Machen’s Warrior Children” https://frame-poythress.org/machens-warrior-children/ (although he meant it as an insult) is cooler than your term of “Machen-ites”. If I were a Presbyterian in the tradition of Machen, I would print up shirts!