The ONLY Reason one might think that Christians share ANY sort of heritage with Islam is because Islam directly rips off OF AND Blasphemes BOTH Judaism and Christianity. Islam actually claims that Jews and Christians misinterprested the word of God, for one, and that secondly Jesus never died on the cross, NOR was he the son of God. THERE is your "shared" heritage.
U.S., allies conduct 1 air strike in Syria and 11 in Iraq against ISIS militants (Reuters)
from the article: Why Christian Zionists really support Israel