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.
from the article: Entering the age of post-aliyah?