And none of the people from these countries have committed terrorists acts against the US?  This is a Muslim ban period.  

And yes the Executive has wide powers regarding security but the Executive cannot infringe on the rights of people who have already been granted visas.  It takes a long time to get a visas from these countries; most of the people suing were already granted visas.  Some were LPRs.  The rules were changed for them arbitrarily and they were denied entrance into the US despite following the legal process.  This was clearly done for discriminatory purposes.  

And as a Republican leaning voter, I think it would be a good thing for the courts to strike down this EO and limit the President's Executive Order authority.  We have three co-equal branches of gov't, not a king.  Republicans were in favor of curtailing executive power only a few months ago.