Well if you were from the Ahmadi or Qaddhi community the issue of who is a Muslim would be pretty pertinent. Also the Sunni/Shia conflict, at the popular level is all about who is a Muslim. As for who is a Christian... the closest I have come to religious persecution was admitting to not being a Protestant at a camp for kids in darkest New England. I was only re-accepted when they understood that "atheist" was not a complicated word for Catholic Spy! All self-identifying groups have issues of identity. Jewishness has them threefold as a biological, social and religious concept.
Report in Lebanon: Israel Air Force strikes Syria's Quneitra, 3 terror operatives killed (Haaretz)
from the article: Defining 'who is a Jew’