Well, but how is it not democratic? Didn't Trump say many times he'd do exactly this, and he won?
Arguably executive orders should not exist, nor should a powerful President. The Swiss system of a rapidly rotating presidency and strong "state rights" seems preferable to me. But the USA has strong elected Presidents and I never saw any American seriously challenge that setup, I hear more talk of states seceding than I see talk of changing the constitution to limit the power of the POTUS.
So I don't see your point. The people were given a (fairly crappy) choice, made it, now their preferences are being implemented. That's democracy.
Don't get me wrong. I think locking people who live in America out of the country because they happened to be on vacation at the time is outrageous, stunningly stupid. But maybe if prior generations of politicians had been more responsive to anti-Muslim sentiment things wouldn't have got so extreme now.