The Zealots were a radical minority of the Jews who hold fervent veneration of the Torah and despised Gentiles and Jews lacking similar religious fervour. Zealots as compared to other religious factions outwardly expressed their hatred for foreign oppression by organising revolts and violence against Jews who conform to Roman ways of life. In my opinion, the Zealots were not of little import ace to Jews in the 1st century CE but held a large importance as the shaping of the Jewish society was concomitant to the works of the Zealots.
The Zealots were dedicated into ousting political control of pagan emperors over the Holy Land, however their actions did not liberate the Jews but succumbed them to a much more terrifying side of the Romans. In order to eliminate these rebellious Jews, the Romans committed gruesome holocausts over Jewish settlements, lynching people, even innocents, suspected of Zealotry thousands of Jewish women and children were sold into slavery; due to the radical actions of the Zealots. This was significant to the Jews as many lives were lost in the Zealots' fervour for liberty, which backfired in the end. A significant event that shaped Jewish history was the destruction of the Jerusalem temple, the epitome of Jewish traditions and faith in 70AD, by Titus, son of the Roman Emperor Vespasian.
Another outtake on the ousting of Rome from the Holy Land was that the Zealots acted as a voice for the Jews that were marginalised by Roman governance. Most Jews, even the Pharisees, would have wanted liberty from Rome, the freedom to establish a Jewish theocracy and rights to go back to a Jewish society not proliferated by Roman culture. Zealots provided a hope for the Jews wanting freedom but did not find the means to liberate the Jews themselves.
The Zealots did not exert their fearsome and violent campaign solely against the invaders but sought to eradicate Jews who collaborate with the Romans or were impious. They encouraged the Jews to take up arms with them to fight the Romans and other Jews for the cause, prior to the destruction of the Jewish Temple. The Jews could not depend on the Zealots to save their lives as they believed in dying for the cause of God, lives lost was just expression to the Romans that they would rather die than to be sold into slavery. In a social aspect, the Zealots did have a large importance and influence in their lives. The Jews feared their fanatical brothers and could have been forced, out of fear, to follow the Law, in order not to be killed.
However, in aspects other than shaping the lives and forcefully instilling religious piety, the Zealots were of little importance to the Jews. The Pharisees at that point of time were the most religiously influential sect, receiving the backing and good-will of the people. The Pharisees were made up of people from the middle class but were treated with deference for their dedication in keeping to the Law, opposing Hellenization in a passive approach which the Jews preferred over the violent doctrines of the Zealots. The Jews continued to adhere to the laws and traditions directed by the Pharisees, said to the most expert and accurate expositors of Jewish law by Josephus.
The Pharisees were considered the champions of the people against the Sadducees. They introduced laws to allow Jews a practical, living faith . Until now, the Jews have been conforming to the same set of rules given by the Pharisees as interpretations of the Written Law. This indicates their high importance to the Jews as religious and political leader, the Zealots were considered but a part of the Jewish society which did not affect the Jews in that matter but resorted to taking things into their own hands.
In conclusion, the Zealots did hold much importance to the Jews as the Jews were instilled with a sense of fear of the Zealots and fear of the harder oppression by Rome in extricating the Zealots. Either way, the Jews were negatively affected, caught in the middle. Even though the Zealots were not regarded as political and religious leaders and did not play a role in shaping their culture, they certainly left a deep impact on the lives of the Jews at that time and were too dangerous to be taken little notice of.