Obama executive orders were done so, and implemented, over a period of time so that the government could adjust and educate in a timely manner. This allowed time to object to them, before implementation. Trump on the other hand is acting like a dictator, issuing edicts without consultation, that are causing people and government to meltdown. His approach is a disaster, and nearly everything he does now will be protested and subject to law suits, because he is doing it unilaterally like a strong man.
On immigration, the problem is Trump is picking and choosing. He absurdly said Syrian Christians were welcome, an outrageous statement, and honestly, how can you prove someone's true religion? He also conveniently left off Saudi Arabia and Egypt, where Trump has business in, but who have exported several terrorists. Secondly, we are already vetting, in most cases it takes YEARS to get into the United States, refugee or not, legally. These people had done their due diligence, and Trump blocked them at the door, really for no good reason. He has no clue how government operates. As for best interest, most with experience feel that the ban will ultimately HARM US interests. Regardless, the vetting process now is about as good as it can be. To expect POOR refugees to even HAVE cellphones let alone to turn over the contacts and browsing history is pretty hilarious. Who is this going to catch? ROFL! These people are not just dumped onto the street, they are sponsored by relatives, as well as often religious groups, same as probably most Americans' ancestors were years ago. The vetting is extreme, unlike obtaining a gun, which is a hilariously easy thing to do, and has cost far more lives than "refugee terrorism." The point though, why couldn't this have been discussed first?
His moves on national security are frankly, frightening. He placed self-professed LENINIST (aka anarchist) Steve Bannon on the National Security Council, while limiting the participation of the UN Ambassador, Chairman of the Joint Chiefs, and Director of National Intelligence. Here again, come the accusations that Trump doesn't give a damn about the facts on the ground OR diplomacy. Sorry, but this is unbelievably insane shit.
As for Obamacare, the Democrats made a calculation. Perhaps it was wrong, but the GOP were unwilling to agree to much of anything in healthcare. They decided that something HAD to be done about the system. They did it. Pre-existing conditions, loss of employment, kids aging but without work, and financial ruin from healthcare costs were ALL dealt with. No the solution wasn't perfect, but here again, Trump's demolish and "rebuild" approach is objected to by even many Republicans. Governors certainly don't want to blow up the system overnight the way he does.
Once more, the protests, which have been largely peaceful, will continue, because Trump's approach has been so awful. He won't change of course. He'll just fire people who tell him to.