Yes they exist and they are influential to things like abortion or gay marriage.
But it's not influential factor in middle east wars.
Middle east wars are related to crude oil.
USA foreign policy is a different important thing, it's not a game of shortterm politic babbling, USA foreign policy is the base of USA empire and it's thought in a long term by powerful interests different to religion: money, oil, military industrial complex and so on.
America has many interest groups, politicians, evangelicals, military, oil industry, etc. but at the top sit the Jews. They convince each interest groups that their proposed policies are in the best interest of each one of them.
They control the evangelical Christians through money and visits to Israel. Their theology had been changed to love the Jews and to expect the return of Jesus.
They control the politicians through AIPAC funding. For the Democrats they promote liberal policies. For the Republicans they promote right wing policies.
They control the oil industry by manipulating oil markets, keeping oil prices high so that the US oil industry stays profitable. Before the US wars in the Middle East prices were too low for oil extraction in the US.
The US military industrial complex benefits from Jewish wars by getting huge budgets. To maintain funding they need to always be at war. The Jews have found dozens of Muslim countries for them to attack.
The Jews in America need Israel to maintain their control over America. If Israel wasn’t there their power would be reduced. That’s why they don’t give US citizenship to Israelis. All the Jews would run away.
So, the power in America is in the hands of the Jews and they maintain control by promoting the interests of all the different centers of power.