Are we as American Citizens, required to defend and support everything Israel does? Can we have independent separate policies? Do we always have to go along? What do you think?
No, you can disagree with the policies of anyone. However the reasons you disagree are what matters in that discussion. If you are grasping at straws to try and justify your objection to the policies, then it has less to do with well reasoned and informed objections, and more to do with a bias.
For example, if you say that Israel is under no threat from Hamas or other radical jihadist groups, then either you are ignorant, or stupid. Ignorant means you don't know, stupid means you won't learn.
How Long Has Israel Been Without Rockets?
Hamas and the radical Jihadist groups regularly fire rockets and mortars into Isreal. They do so in the hopes of provoking a response, and then the press is given access to show what the Isrealis have done this time.
List of Palestinian rocket attacks on Israel, 2016 - Wikipedia
Palestinians have had plenty of opportunities to live in peace, and they instead have dedicated themselves to eradication of the Jews. This conflict between the two has been a fact of life since the Isreali's declared statehood in compliance with UN Resolution 181 in 1948. The Islamic nations and peoples used that declaration as an excuse to do what they had been prepping for anyway. They launched attacks to destroy the Jews, and we helped the Arab nations. Don't pretend we didn't. We did everything we could to limit access to aircraft, weapons, munitions, medical supplies, food. The RAF flew reconnaissance missions over Israel. This wasn't to help the Jews, it was to provide intelligence to the Egyptians, the Syrians, the Jordanians, and the Palastinians.
Everyone assumed that Israel would lose, but they won, and won again, and defeated armies that outnumbered them by impossible factors. Personally I think Israel will win again and again in the future. The reason is simple. Sun Tzu calls it Death Ground. The Israeli's have no where to go. There is no where for them to retreat to. No where for them to seek sanctuary, and no one who will provide succor. For them, it's victory, or death. This reality tends to focus the mind, and turn good soldiers into great soldiers. Those soldiers fight as if they have nothing to lose.
The Japanese saw this first hand in World War II on Guadalcanal. The Americans saw it on many other islands. It was victory, or death for the defenders. The Palastinians know they can withdraw to Egypt or perhaps Jordan. They have a door open to escape. The Israeli have no door, no escape, no option except determined defense.
I believe that the Israeli people would be happy to live in peace. The rub there is that the other guys have to want to live in peace too. The Palastinians want piece, that is to say pieces of Jews scattered all over.
Watch the documentary called "Above and Beyond" to see what it was like trying to get an Air Force started for Isreal.