After undergoing the horrors of the Holocaust in Europe, it is no wonder that the Jewish people felt the need to have a land of their own. The Nazi persecution was truly the impetus to return to Israel after the war and feel safe in their own ability to self govern.
Yes Israel was a result of Nazism. The Israelites had been rounded up and left without a home . They needed to have a place where they were safe and could live in peace. As a result the mation of Israel was created in order to give the Jewish people a home.
The relocation of European Jews out of Europe and into the Middle East was definitely a reaction to Naziism, although the fall of Naziism itself greatly reduced antisemitism in Europe and the Western world alike, whereas the creation of the state of Israel over occupied Palestine managed to cause antisemitism to flourish in that part of the world. It's a vicious cycle, but ultimately the answer is yes.
The state of Israel was created as a Jewish homeland to try to prevent another Holocaust. The only difficulty with that is the people who already lived there had to go. The United Nations, as well as Europe, didn't think of the long-term consequences of their actions in regards to the Middle East. Israel wasn't created because of Nazism, it was created to give Jews a place to live.
No, the State of Israel was not created in response to Nazism, rather it was to fulfill the will of God that the Israelites return to the promised land. It was predicted in the Bible that the Israelites would be scattered, but that they would return to their homeland. The creation of the nation of Israel was God's will for the last days.