I think I ought to revisit this before it gets too far away and I forget about it. I'm not sure it's entirely accurate to say that this is merely an "assumption", either on my part or on the part of the courts. I'm not simply assuming, in the absence of any support, that the 14'th applies the establishment clause to the states - that is the law. It's sort of like objecting that I'm just assuming that a carrot is an edible orange vegetable that grows underground and has a long, tapering shape to it. That's not an assumption - that's what a carrot is, as a matter of definition. The courts are responsible, at the moment, for defining what the meaning and applications of the 14'th amendment are - it's not an assumption on their part any more than the nature of a carrot is an assumption by the folks at Webster's. Defining it is what they do. We may disagree with their definition, but that really doesn't make it an assumption, nor am I simply assuming that this is the law when I report it to you - that is, in fact, the law, by definition.
I call it an assumption on the part of the courts because they give no reasoning to support it. Yes, they give some somewhat credible reasoning to support the notion that the 14th applies the free-exercise clause to the states, because if you're arrested for giving a Hail Mary you can say that you've been deprived of "liberty" without "due process of law" and all that jazz.
But then the courts simply make the assumption - I chose the word deliberately - that since the 14th applies the free-exercise clause, it must also apply the establishment clause in the same way, with no evidence that I've seen so far to suggest that they've subjected that assumption to any kind of critical examination. How does a state's promotion of a religious belief - in a non-coercive way - violate someone's due process? They don't answer. You've begun to answer, and I appreciate that, and I've begun to address that answer in my post above. But everything I've seen so far fully justifies my use of the word "assumption" to describe SCOTUS's methodology.