Defenders of the Manhattan Declaration have been posting a lot of bad arguments in response to the controversy over the document, in addition to largely ignoring the best arguments against their position. One argument I've seen is an appeal to 1 Corinthians 15:1-4, as if the passage demonstrates that a group can reject justification through faith alone, yet still be orthodox.
Evangelicals and Catholics disagree significantly over what "died for our sins" (1 Corinthians 15:3) means. As the book of Galatians illustrates, the adding of works to the gospel nullifies what Paul summarized in 1 Corinthians 15. As he puts it elsewhere in 1 Corinthians itself, the gospel involves the sufficiency of the crucified Christ (1 Corinthians 2:2). Paul defined that sufficiency in a way that made the inclusion of works as a means of attaining justification a denial of the sufficiency of Christ and His finished work. Any understanding of 1 Corinthians 15 that makes the Judaizers orthodox is problematic.
For an explanation of why the Roman Catholic gospel is false and why it should be considered to be under the anathema of Galatians 1, see posts # 94 and # 99 in the thread here.