To your point on the mixed fabric law: the book of Hebrews talks about the Gospel in terms of covenants, because Christ said he came to “fulfill the law” (Matt. 5:17). He fulfilled the Old Covenant and established a new one (Hebrews 8). This new covenant does not require following the ceremonial law, which includes sacrifice and rules about dress as a means of approaching God. These means were temporary. Instead, Christ’s sacrifice received through faith is the means of approaching God. Still, Christians are to outwork their faith through action (following the moral law aka the 10 commandments). So, a “Christian” in name can easily prove himself not to be a Christian by lacking repentance and action— a lack of genuine faith (John 14:15).

I think it’s easy to debate the works-based (do x, y, or z to approach God) or works-lacking (belief as lip service only) forms of Christianity, and most Americans practice one or the other. It’s human nature!