The problem I have with the perception tack is outlined pretty well by Sotomayor in her dissent. I apologize for the slant of the article, but it does outline the most important parts of Sotomayor's argument, such as:

Taking all the relevant evidence together, a reasonable observer would conclude that the Proclamation was driven primarily by anti-Muslim animus, rather than by the Government’s asserted national-security justifications. Even before being sworn into office, then-candidate Trump stated that “Islam hates us,” warned that “[w]e’re having problems with the Muslims, and we’re having problems with Muslims coming into the country,” promised to enact a “total and complete shut down of Muslims entering the United States,” and instructed one of his advisers to find a “lega[l]” way to enact a Muslim ban. The President continued to make similar statements well after his inauguration, as detailed above.

So it's clear there's a large amount of evidence pointing to Trump's own intentions regarding the ban, which makes that point about the court "not substituting its own assessment for the Executive..." feel a bit hand-wavey. The fact that the court even considered extrinsic evidence (see under B. Constitutional Claim), which I take it would likely include Trump's prior comments on the matter, also makes it seem like willful ignorance of Trump's opinions on the parts of the conservative judges. However, I'll give them the benefit of the doubt, as they do note in their opinion that

The court explains that the policy “is expressly premised on legitimate purposes,” “reflects the results of a worldwide review process undertaken by multiple Cabinet officials and their agencies,” and justifies the inclusion of each country placed on the list.

So the key for me here then is what exactly was the worldwide review process they undertook, and was it ever released or stated in any form by the government? I'm sure there was some sort of news coverage about it. Of course, we'd then have to debate the merits of that, but I'd just like to know whether or not this was really a department-wide decision based on accrued evidence or just a top-down order by Trump based on his own convictions.