This has happened in Ireland too
I live in Ireland which, as you may know, was the scene of many years of terrorism both here and across the water in the UK. I see some parallels with what is happening now.
I won’t go into the complexities of the issues at stake because that's not important here. The key comparison I want to make is with the way Irish people were treated during the ‘Troubles’, as the era was called. Many bombs were planted in London and other cities over a period of many years, most of which caused civilian casualties. Not surprisingly feelings ran very high. (I had a narrow escape myself.) Yes, you did get everyday Irish people being asked if they that was a bomb in their shopping bag. It wasn’t pleasant but I don’t think you’ll find any country in the world that wouldn’t react in similar ways (and possibly much worse). Muslim countries are no different.
There were then, and still are today, many people of Irish descent or nationality living in the UK. At times they experienced negative reactions. Although they were not especially marked out by appearance (as some Muslims are in the US) Irish people have a very distinctive accent. Certainly, there was a time when a Northern Irish accent was not a good thing to have.
Unfortunately, many English people could not tell the difference between a Southern and Northern Irish accent, so many southerners also became objects of suspicion. Also, ironically, half of the Northern Ireland population are Protestants who are loyal to the UK – yet they too were mistaken for being potential Catholic terrorists (the IRA).
The effect of this was that many plainly innocent Irish people experienced discrimination and negative reaction - just as innocent Muslims are today. In fact this is one of the objectives of the terrorists. The IRA knew perfectly well that their actions would make life very difficult for moderate Irish people living in the UK. They hoped that this discrimination would itself radicalize more people and drive them into a more extreme mindframe. The same tactic can be seen with Muslim terrorist groups today. You have to say it's working.
Irish people became objects of suspicion (and there were many, many more bombs than America has so far experienced so the provocation was far greater). However, it was never so bad that Irish people felt they had to leave the country in any noticeable numbers.
What is truly remarkable is how quickly that anti-Irish prejudice has passed. The Troubles have been over for about 10 years (apart from isolated incidents). Irish people have not only rapidly ceased to be regarded as security risks, but Ireland has even experienced a kind of weird ‘trendy’ phase (although that is also passing as these things do). You will find many English people who positively identify themselves as being Irish, even though their relationship is minimal. Being Irish is popular. Even in the very cities that were bombed.
For that reason I think the anti Muslim sentiment in the US can pass very quickly in the future, if other conditions fall into line.