The president has broad power to control immigration policy in the united states, however the recent executive order has a number of problems, even if you are for reducing immigration and travel from traditionally muslim countries.  It appears the administration did not do a good job vetting this EO in terms of legal or administrative implications, that is why the courts are issuing injunctions against it.  Once those kinks are worked out there is still a much bigger legal issue of if it is constitutional to a have a religious test (i.e. exemption to the ban for christians and other non-muslims).  There is of course the larger policy question of if it really protects america or has the opposite effect of threating our security by isolating us from our allies.

Some of the protesters probably are whinny  brats, however most are just americans concerned with making sure this country lives up to the ideas enshrined in the consitution and on the statue of liberty.