So long as it wasn't presented as a scientific alternative to Darwinisim. Unfortunately, that's exactly what the Dover board did.
If I read your position correctly, you're arguing that the 14th did apply the Establishment Clause to the states, but the widespread practice of public school Bible reading, prayer, and direct aid to religious schools weren't an Establishment violation.
So long as the bible readings and prayers weren't sectarian in nature, no. Direct aid to religious schools would be okay so long as the state did not discriminate against any religions, except those that have doctrines contrary to the public interest (i.e. Christian science, scientology, satanism, fundamentlist mormons, jihadist Moslems, etc). The safest way to do this would be a voucher system, which I believe SCOTUS has ruled does not violate establishment.
If none of those are a violation, how could it be one to merely mention ID alongside evolution?
Because ID is a sectarian religious doctrine with no scientific basis, rejected by many religions, whereas evolution is a scientific theory with a mountain of evidence behind it. To mispresent ID as a scientific theory as equal in status to Darwinism, therefore, tramples on the rights of those Christians who reject it as bad theology mascarading as pseudoscience.
I really don't see how it's any of the federal courts' business under the First Amendment (even if we accept the controversial argument that the Fourteenth Amendment applies the First to the states) to inject themselves into this political debate. Some religions say we evolved, some say we were designed. Science, despite all the bluster, doesn't know for sure. Leave it up to the local voters.
The solution, theoretically, would be vouchers. However, we all know what would happen in reality if the public schools were replaced by private schools. The ACLU and the evolutionists would announce that the vouchers are aid to the schools, so the private schools have to adopt the same secularist policies as the public schools. There's literally nothing that would ever restrain the evolutionists on this. If the private schools managed to somehow survive without vouchers, the evolution crowd would claim that the point where the school's private driveway connects to the city street is a "state benefit" and thus the entire school falls under secularist federal control.
It's obvious from these lawsuits that we're dealing with fanatics who simply can't conceive of a world where their view isn't protected from competition by government power. People like that don't give up easily.
Our only hope is to get judges such as Alito (whom I'm confident will join the Scalia forces on this issue) on the court.