One of the reasons why Theodor Herzl started the movement for a Jewish homeland was European anti-Semitism. A non-Halachic Jew with a Jewish name can be a victim of anti-Semitism and should therefore be welcome in the State of Israel. When your name is Goldstein, it doesn't matter if your mother is a Jew or not. The outside world thinks you're Jewish and will act accordingly.
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IDF: Shots fired at troops operating near Gaza border, no injuries or damage sustained (Haaretz)
from the article: Entering the age of post-aliyah?