The fact you assert undeniability doesn't make it so. Your rationale is entirely dependent upon your assertions. So it is a brittle approach. Usually these things - you know, things to do with the law - are founded upon legal arguments and supporting evidence, as well as arguments and evidence to the contrary, rather than assertions which the author presumes are quasi-scientific and thus unarguable.
This is why there are various lawsuits suggesting a variety of flaws in the EO. The courts will decide if the EO is lawful.
In my opinion, the most important evidence suggesting that the EO was a ruse disguising a religious test was Rudy Giuliani's statement expressing that this is the case. This combined with the exceptions for non-Moslems means this legal argument may take place in the territory of the establishment clause.
Then the question is, does this affect the lawfulness of the EO? Perfectly reasonable question. The AG decided it did for jurisprudential reasons.
Perhaps you are a constitutional scholar and we must defer to your expertise. My impression is that the two of you newcomers have a weak understanding of how the law works. Because your whole approach depends upon a rookie understanding of legal argument. You think it springs from your unsubstantiated assertions. You don't even begin to question your premises, provide evidential support or address the counter-arguments. So your assertions lack force. They just come across as partisan statements intended to bully clo, myself or anyone that disagrees with you.
Why not start over and consider the different arguments about the lawfulness of the EO? Maybe start with the Yates memo, the ACLU and the Washington State suit. See how you fare when you actually address issues rather than assert an opinion. And remember to be respectful of folks with whom you disagree. Maybe you will learn something along the way.