If your passport shows a stamp from a country (like SYRIA) who is a sworn enemy of Israel, you better have a good explanation for why you are visiting Israel. If you act shady (even out of nervousness), the border patrol can, and should, deny you entry. Millions of tourists come to Israel every year, many of them leftist anti-Israel types, including Muslims, and the vast majority are allowed in. Stop twisting this story into something that it isn't.
Condition of woman seriously wounded in Jerusalem stabbing attack slightly improves (Haaretz)
from the article: American Jew refused entry to Israel on suspicion of converting to Islam