Israel does prevent those with sympathy to the Palestinians from entering Israel.

I posted this quote/article in response to another comment but it is pertinent here:

"The agent, suspecting Tamari was involved in pro-Palestinian activism, wanted to inspect her private email account for incriminating evidence. The 42-year-old American of Palestinian descent refused and was swiftly expelled from the country."

http://www.timesofisrael.com/pro-palestinian-activist-says-s...