Here is Brian Schwertley talking about headcoverings and doctrinal compromise:
One could walk into any first century Christian church, whether in Asia Minor, Palestine, Greece, or Rome, and observe a lesson in covenant headship and the Christian family. Sadly, the opposite is true today. Modern declension can be observed in most churches every Sabbath because the apostolic injunction is rarely observed. Feminism and sloppy man-pleasing exegesis have contributed to the widespread disobedience to apostolic authority today. The only remedy for such rebellion against this biblical imperative (see 1 Cor. 11:6b) is repentance.
Note also that unlike modern Reformed churches, which teach and practice diversity on this issue, Paul demands uniformity of doctrine and practice. The apostle says that if anyone seems to be contentious (i.e. disposed to quarrels or dissentious argumentation) about this matter they must stop and submit themselves to apostolic authority and universal church practice. Paul understands that there are people in the church who disagree with his teaching on headcoverings. He recognizes that some people may even be angered by his doctrine. This recognition, however, does not cause Paul to act like a spineless modern church bureaucrat who attempts to ride the fence on controversial issues. Rather, Paul stands on the inspired truth of his argumentation and demands uniformity of doctrine and practice on this matter. Biblical unity is established on the teaching of Scripture. Real lasting unity can only be achieved when believers submit themselves to the authority of Scripture.
The modern idea that unity is accomplished through compromise, through allowing mutually contradictory practices and doctrines in the church, is rejected by Paul. The inspired apostle knows that his arguments for head coverings in worship are not based on contemporary usages, but on biblical truth and creational realities that will last as long as the present earthly economy. The covenant headship of the husband over his wife and the purpose of the wife is the same today as it was when Paul wrote this chapter (1 Cor. 11:7, 8, 9). A woman’s beautiful hair is still given to her as a natural veil, as her glory, as it was in times past (1 Cor. 11:14-15). The divine order of authority from the Father to Christ and from the man to the woman obviously has never been abrogated (1 Cor. 11:3). The angels of God still observe the public worship of God as they did in the first century (1 Cor. 11:10). When we consider the apostle’s careful argumentation, brilliant reasoning, sublime analogies and authority as an inspired teacher, we can understand his dogmatism and unwillingness to compromise on this issue. For Paul to allow diversity of teachings or practice on this issue would be to admit that he was totally wrong in his reasoning. For modern churchmen to allow diversity of practice on this issue is to implicitly deny the perspicuity of Scripture and apostolic authority. Modern believers who profess that they believe in the inspiration and authority of Scripture, yet who want to argue with the apostle Paul about his teaching on head coverings must repent and submit to the inspired command of Christ’s chief apostle: “Let her be covered” (1 Cor. 11:6).
Read More: The Head Covering in Public Worship by Brian Schwertley (pdf)