Controlling who gets in to the country is why we can have nice things like constitutional rights.
The US under Abe Lincoln during the civil war, being a warzone had large areas where constituional rights took a backseat to military necessity.
In the interest of keeping the US not-a-warzone, we need to prevent enemies from entering. It is better to make rights violations a condition for entering than to be forced to abandon rights at all points within the jurisdiction of the US.
And anyway, the constitution only applies to the Jurisdiction of the United States. If you've no visa and are outside the US borders, you have precisely zero constitutional rights. There was a 1980s SCOTUS ruling about that, so it's a pretty solid foundation to base extreme vetting on.
If you have some prior relationship with the US such as a previous visa you MIGHT be able to make a case that you are somehow under the Jurisdiction of the United States and so due constitutional rights, but that's pretty iffy.
IMO, having read through the Koran, it seems obvious that anyone who simply does what it says would be an enemy to me personally and to the values and culture I think have been and hope will always be inherent in what it means to be American. Moderate Muslims are lying to themselves. Maybe some day they will find their way to secularity. But it's not my problem if they stay out of my country.
The constitution was written in the absense ( to a number of decimal places ) of Islam.
The absense of large numbers of Muslims is one of the reason we can have nice things like constitutional rights.
We should do what we can to defend what we have inherited from the enlightenment, and preserve it for future generations.