Can you clarify what you mean by birthright citizenship? Children born in Germany generally are German citizens so long as one of their parents has been resident for a while.
Do you mean a system where just being born in the nation, regardless of circumstances or status of parents or even how long you were there, makes you a permanent citizen? If so, I don't think the lack of such an unusual law is something you can say is against socialist principles. It's a rather irrelevant thing to mention. Right or left wing, fully open birthright citizenship is a trait of the new world- i.e. the Americas and is more related to their attempts to populate the nation than any overarching political philosophy.
But in any case, as pointed out, Germany isn't really an example of a socialist country.
Not quite sure I understand your main question either- Germany is exceptionally welcoming to immigrants. It's why they take so many. The concern now is over the high volume and distribution, not the principle.
The big problem with EU immigration right now is that a lot of EU countries signed a legally binding agreement saying the first signed-up nation where an asylum seeker arrives is the country where they will find asylum. But as jaden says, that's doesn't exactly work in nations like Greece who can't possibly manage the influx, and who are now ignoring that law and moving asylum seekers on.
This has wider political ramifications- Germany is talking about altering the EU treaty to adapt to the new situation. The UK has been after treaty change for years to settle its own relationship issues with the EU, including immigration. Most nations have been against going through the hassle of treaty change just to keep the UK happy, but this creates an opening to settle everything.