Legally, I doubt that this is enough. I Am Not A Lawyer^TM, but I gather that courts don't generally take account of arguments that rely on evidence of hidden intent unless there's truly a smoking gun. The text of the executive order carries most of the weight, and the president has extremely broad authority in immigration law. Most likely, the bulk of Trump's order will remain in effect.

In the court of public opinion, however, the evidence suggests pretty strongly that Trump's order was, in fact, little more than a thinly disguised attempt to ban Muslims from the Middle East--except for those from a few favored allies. Pretzel-bending arguments aside, it's really pretty obvious what's going on here.

The stay by the judge in Brooklyn gave a hint in that she wrote there was a strong likelihood that the two plaintiffs who were seeking to represent a class of refugees, visa holders and others, could establish that their removal would violate the due process and equal protection Constitutional guarantees.

Also, the stay included the statement that "irreparable injury" would be caused. The judge's injunction barred removal, but did not order release. Other judicial stays were either broader (Boston) which barred removal and detention, or narrower, (Alexandria) which applied to permanent residents.

The president does have broad power to control immigration, including suspension of aliens or a class of alien immigrants if detrimental to the US, but that power does not include discrimination on the basis of race, sex, nationality, place of birth, or place of residence.  

Carving out green card holders strengthens Trump's case; and there is the matter of standing--not favorable for foreigners outside the US, although states/businesses may attempt to claim damage. And, US citizen relatives of foreigners may have standing.  

An issue of dispute will be claims of motivation. Establishment of religion issues may be pursued since the executive order appears to grant exceptions to minority religions--favoring Christians over Muslims. Although, it is not clear if this applies, also, to Alawites/Shia and Sunni. Trump will need to build a better case than he has done in the rush to portray his anti-immigration creds.

In any event, it is likely to fall on the Courts to sort all of this out.  Clearly, the Trumpkins, Cabinet officers, and, in large measure, Republican officer holders are either missing in action, or busy nodding in agreement--whatever the law may be.