It's a complex issue, but in short, I think that some of the concerns about immigration are often legitimate.
Progressive people, being more keen on altruism, tend to think that the good reasons immigrants have to migrate should overshadow the problems that immigration can cause.
And sometimes there's maybe also a view that a strongly multi-ethnic society is something to aspire for, because of the increased understanding of different people and hopefully a reduction of racism that it can lead to.
Progressives tend to think that everyone should be as tolerant as them, and that can lead to only looking into the problems, and finding solutions, up to a degree.
I saw that in the shift from arguing for integration to arguing for tolerance and a multi-cultural society, for example, where inadeguate integration efforts faiiled.
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On the other hand, right wing/conservative parties often enact policies that compound the immigration problems, rather than improving them.
In part that's due to a preference for securitarian policies, rather than looking for the root causes.
And in part that's because immigration problems most often lead to increased votes for them, so it's in their interest to not actually solve them.
All this, in the end, can create a space for parties standing for drastic solutions such as mass deportations; however immoral, dangerous for everyone and hard to realize they may be.
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The way forward, in my opinion, should be for progressive parties to stop dismissing the problems that immigration can lead to, and to do their utmost to improve them all, rather than pretending for everyone to be as tolerant as them.
The actual middle/long term solution would probably be ensuring that the new potential immigrants are willing to integrate to a sufficient degree, and most of all to look into what pushes them to migrate in the first place, and work for improving the causes of that.
The latter can seem utopic, but it's better than the alternatives, in my opinion.
Ok, that wasn't so brief xD