The snarky response is that I believe Israel exists because it can be demonstrated that it does, unlike deities. However I suppose you mean to ask if atheism results in a lack of support for Israel.

I'd respond to that as follows: my support or lack thereof for Israel's right to exist, or for its specific actions, depends on the facts in evidence, and their actual conduct, not on tradition or automatic deference to religion or religious heritage.

In general, I'm not impressed. They seem to be basing their actions on fascistic authoritarianism and hatred of outsiders rather than following any sort of ethical or moral compass. In that sense I suppose, yes, ironically they are something like Nazis. I'm not any more impressed with the region's Arabs, though.

Historically speaking, there NEVER was a land called Israel in the Middle East. It only came into being after WWII when Britain, France and Russia wanted a solution, less controversial than the Nazi Extermination, to the Jewish Problem that had plagued Europe for centuries, i.e. give them someone else's land.
America saw in the Balfour Accord a way to SELL arms to yet another customer and quietly agreed to it since most banks and industries in America were owned, either partly or completely by Jewish Consortiums.
Hence they decided to USURP Palestinian Lands and hand them over to the Jews.
The present name, Israel, is derived loosely from a very ancient terminology used throughout the Middle East as a disparagement for the Hebrews, i.e. Ishmraeli = the untrustworthy, the ones who always beg, steal and refuse to work, the thieves, the child abductors, the slave dealers, etc, etc.
I was very common knowledge throughout Ancient Egypt in particular that Hebrews could be regularly expected to arrive enmass when the Egyptian Harvests were greatest and claim sanctuary from famine then enjoy the charity of the Egyptians for as long as they could before wandering back to the desert lands.
Ancient Egyptians likened them to 'Sand Crawlers,' i.e. scorpions, a pest of the highest order to be tolerated only because of the Rule of Ma'at, the Egyptian Law of Universal Harmony and Charity.
Even up to the Roman Empire in the Middle east and much later in History, the lands the Jews now falsely claim were known as either Palestine or Canaan and divided into Judeah, Galilee, etc, BUT NO Israel, and according to Hebrew Law ONLY those who were born within the precincts of the small and unimportant town of Jerusalem could truly call themselves "Jewish."

Best example of how all religion is evil, and destroys everything it touches.

Honestly, I don't care if they all kill each other.
I wish this government would quit supporting everything in that region. Don't send any if then another dime.
Cut them all off and let them figure it out.

I don't support the policies of the Israeli Govermnent, and I do have great sympathy for the plight of the Palestinian people. I don’t hate Jews, but I find the fact that the Jewish State seems to be pursuing the very policies that led to Naziism in prewar Germany disturbing, I lay a lot of the blame for much of the current problems in that troubled area of the world, at the door of France and Britain who carved up the territories of the Middle East at the end of WW1. Then, after WW2 and a terrorist campaign by Zionists, Britain ended its mandate in Palestine and the United Nations voted to grant Jews their own state which became Israel. The Palestinians were given a raw deal in my opinion and were left with a small amount of territory, ever since which Israel has encroached and built on. There were constant wars over a number of years between Israel and the other Arab States who backed Palestine and each time Israel gained more territory and have consistently ignored UN directives not to built and settle on Palestinian land on the Golan Heights. The Palestinians are now virtual prisoners in the Gaza Strip with the Mediterranean Sea on one side and Israel on the other. At times the Israelis blockade the port at Gaza and prevent supplies getting in and at all times the Israeli Navy have gunboats patrolling the coast of Gaza. I never condone violence, but in the case of the Palestinians I find it understandable. They are firing rockets into Israel, but they are like pea shooters against the military might of nuclear powered Israel.

Actually if we want to get technical that land should’ve went to Ishmael but through manipulation it went to Isaac who’s son betrayed his brother to become the leader of then people supposedly founded it.

And even then it appalls me that Russia looks like they’re targeting the Ukraine and everyone is like arm the missiles but Israel is constantly invading other countries and we’re like we should give them more weapons and money. SMFH

Even when I was a believer, I did not believe that anyone has the right to kick people out of their country because a book told them that someone else should be there.

It just never made any sense to me.

No. Many Jews are agnostic atheists. Also, most rational people support Israel as the only functioning democracy in the Middle East. It is surrounded by fanatical nations who wish its destruction.