No country has 100% free borders. There are two conditions under which people can have their freedom of movement justly curtailed ... either they have been convicted of a crime or in the (much rarer) case that someone has a severe communicable disease. Both of those are causes to keep someone out as well (assuming they aren't coming in under quarantine procedures to begin with for treatment).
However a person's beliefs are their own business. No one is a criminal until and unless they *act*, or in some cases plan an action, that would harm the person or property of another.
If you ask a Muslim in a country where strict Sharia is the law of the land if they approve of strict sharia law being imposed on everyone, it would be surprising if they said no. If you ask most Muslims living here, the answer most commonly *is* no. People self select in deciding where to go.
Even for those Muslims who support Sharia as formal law, most do *not* think it should be imposed on non-Muslims. Nor do they all have the same interpretation of what Sharia law actually covers. There are less than a dozen countries around the world that actually codify *strict* Sharia into formal law. Most countries that implement Sharia via formal law only use it for family courts and secular for the rest or have separate family courts for Muslims and non-Muslims.
For a good overview, go to this survey analysis.
Not one person from any of the countries on Trump's (and formerly Obama's) list has ever killed an American in an act of terrorism on our soil. Not one.
As to social changes, going to America is a far different thing from going to an EU country. It's much easier to get from Africa or the Middle East to Europe - just a few hours to less than a day, depending on where they start from, by boat. Many EU countries have very generous welfare benefits right from day one for immigrants, no matter under what circumstances they got there. Many European countries have turned a blind eye to having Muslim dominated areas where at least some of sharia has been self enforced.
Yes, they dress differently and pray differently, but in essence, how is wearing a hijab any different from an Amish woman's cap? How is a full beard any different from an Orthodox Jewish man's payots (long curls and back hair)? How is praying 5 times a day facing Mecca any different from saying Grace before every meal? How is a Mullah's call to prayer any different from Sunday church service bells? How is Ramadan any different than Lent? How is the violence called for in the latter parts of the Koran any different from the violence being called for in the Old Testament that led to the violent conquest and forced conversions in Europe and the Crusades? The vast majority of people today seem to have no problem separating those parts out and not actually acting on them and so do most Muslims. I'm also no more surprised to hear that an Imam may call for the Qur'an to be law than I am for a Fundamentalist Minister to say the Bible should be the law of the land.
Note: I am *not* saying that we should not give the background people from a region that is a hotbed of terrorism an extra going over. I have no problem with that. I have a problem when people assume (wrongly) that all Muslims are terrorists almost by definition.
The biggest problems I have with Trump's ban is that it also included people who were already legal permanent residents (green card holders) and those who had already been granted a visa as well as exemptions being made and prioritized on a religious basis. I don't really like the blanket ban on new visas or refugees for four months for six of the countries and indefinite in the case of Syria, but I could live with that part of it while improving our vetting procedures.