Europe and US are quite incomparable when it comes to immigration. In the US immigrants tend to integrate well, in Europe certain types of immigrants integrate extremely poorly.
The right in the US uses Europe as a supposed example of what it would be like under democrats / the left, but that's completely untrue. The situation is completely different.
The big majority of people in Europe do think there are big immigration issues...because there are. The cause is extremely lax immigration laws, compared to the US which is a lot stricter and requires people to integrate to get citizenship. While the US tends to rather attract the good layers of people from certain Muslim countries ("modern people"), a lot of the immigrants in Europe are people who are even considered "trash" in their own country (obviously not all). Which is people from poorer rural regions who are more extreme in their religious views, strong patriotism, poorly informed and easily manipulatable with propaganda (basically the Trump supporters equivalent of their country). In addition, the extremely lax laws against immigrants and criminality also attract criminals from abroad. I.e. let's take Marocco as an example: some thieves from Marocco travel to Europe to steal there, not necessarily because they want to live there but because they can make more money in Europe with relatively little risk: unlikely to go to jail for the first offense, better jail conditions, shorter sentences, etc... (a lot less risk).
What Europe needs is to be a looooot stricter on the terms they set for immigrants and to also set standards (the immigrant must have value to the country they want to integrate in). The "bad immigrants" do not only cause mayhem themselves, but they also make it a looot harder on "good immigrants" by causing discrimination and immigrants to "stick together" rather than to integrate with the rest of the community. Europe needs to keep the trash out while allowing "the good ones". Currently, not rarely some criminal immigrants are allowed to stay while a hard-working well-integrated person can get extradited because of ridiculous rules and actions.
And yes, we have a far-left which pretends like there aren't any problems and which pampers immigrants to extreme lengths. But these people aren't comparable at all to Berny Sanders, democrats or what Americans call the left or liberals (they're waaaaay more to the left compared to those). The US doesn't really have an equivalent to them. It's just the far-right who misrepresents it to scaremonger people.