Is Trump’s Executive Order Declaring American Jews as a Race and Nation Constitutional?

No. To begin, no president has unlimited authority. President Trump disagrees—but he has lost most of his executive order cases because they exceed the scope of his powers.

But what about this order is unconstitutional?

Let’s start with where a president’s powers are greatest— his role as Commander-in-Chief. But American Jews are not at war with anyone. This is not a military case. So that’s a practical problem for Mr. Trump.

Let’s explore that for a moment. Even in that sphere, there are limits on a president. 
Remember the travel ban/Muslim ban? The Supreme Court upheld it. But in that case, it overturned its Korematsu case (WW II Japanese internment camp case), going so far as to call it racist. This executive order isn’t racist—but who gave the president power to declare any group a “race”?

Now let’s get to the core constitutional problem here. The president and some American Jews believe that universities discriminate against Jews by promoting a Palestinian campaign to boycott Israel. Practically speaking, the Palestinian cause would prohibit universities from bringing in Israeli faculty, students, and speakers. President Trump wants to punish American universities who allow or promote the Palestinian boycott idea by withholding all federal funds. 
But he concedes that no law allows him authority to do that. Funds can only be withheld to schools that discriminate on the basis of race or nationality. 
Hocus-pocus-poof! Problem solved: Jews are a race. Jews are a nation. Palestinian boycotting, supported by universities (a fuzzy idea to begin with), leads to defunding these schools.

And here is the bottom line: When a president tries to circumvent a law passed by Congress by declaring an executive order to the contrary, courts strike down the executive order.

Just ask Bill Clinton. He implemented an executive order barring companies who hire permanent striker replacements from getting federal contracts. I wrote at length on it in "Presidential Regulation of Private Employment: Constitutionality of a Executive Order 12,954 Debarment of Contractors Who Hire Permanent Striker Replacements," https://lawdigitalcommons.bc.edu/bclr/vol37/iss2/1/). The D.C. Circuit Court of Appeals said no president can contradict a law, and struck down Clinton's order as unconstitutional.