In the run-up to Dobbs, I identified many areas of the law that abortion had distorted. Among these epicycles were stare decisis, freedom of speech, facial challenges, the tiers of scrutiny, third-party standing, and so on. Dobbs, thankfully, ended these epicycles. (Alas, some litigants are trying to drag religious liberty into the fray.)
Like abortion, the Supreme Court's doctrine concerning the Establishment Clause has distorted other areas of the law. As a threshold matter, I'm not even certain the Establishment Clause can be incorporated. I think the better answer, as Akhil Amar has written, is that this federalism provision prevents the federal government from interfering with state established churches. But that ship has probably sailed. Perhaps the most obvious category of distortion is standing. Flast v. Cohen allowed a taxpayer to contest government spending that may run afoul of the Establishment Clause. Flast is an anomalous outlier to Article III that permits taxpayer standing.
A related distortion of standing doctrine concerns the "offended observer" standard. In short, if a person sees or hears some government-related religious content that offends him, he has Article III standing. For example, Thomas Van Orden was an atheist who walked past the Ten Commandment monuments by the Texas Capitol. Boom, standing! I have long questioned standing in cases like Van Orden v. Perry. And more recently, Justice Gorsuch cast doubt on this doctrine in American Legion and Kennedy v. Bremerton.