But they're already in, legally, according to the laws you defined? It's hard to believe that you have such a well-defined social contract that literally everyone agrees that means you can't let in people of another ethnic group if the laws made by the people you suggest literally don't support mass deporting everyone who fits into the group you mention.
Scandinavia is in a much better spot than the UK, which voted in favor of brexit to stop flow and instead received replacement migration.
When Scandinavia entered Schengen it was all Western European countries that explicitly kept Eastern European countries out.
Asylums were rare, low in number and strictly enforced to known political refugees with very few arriving until the UN started funding migrant transports & EU started requiring quotas from the third world through EU at the risk of severe fines if you say no.
There was no vote on these changes to what was previously very strong borders.