Palestinians there have told Euronews they fear arrest if they were accused of speaking out about the war - including liking or sharing messages on social media platforms.
Critical Israelis, including university lecturers, journalists, and politicians, said they have already been targeted just one month into the conflict.
Arab-Israeli politician Aida Touma-Suleiman, who has condemned Hamas' attack on Israelis, said she was prevented from showing similar compassion to Palestinians in Gaza.
“I don’t have walks with my grandchildren anymore because I don’t want anyone to know they’re my grandchildren,” she told Euronews' Shona Murray.
“There's a huge incitement against anyone who dares to protest against this war or to even reveal a little bit of empathy toward what is happening in Gaza.
"We are not allowed even to cry for a Palestinian child who is killed there.”
A task force designed to monitor hateful speech against the state of Israel was set up in February by National Security Minister Itamar Ben-Gvir.
And in recent weeks, the Israeli court system has upheld the remand of those accused of breaching the law – judges say it’s necessary given that the country is in a ‘time of war’.
Amir Badran and Itamar Avneri are Palestinian and Jewish political allies who are working for a joint approach to tackle fear and hatred which has gravely deteriorated between the two communities.
“Jews and Arabs are afraid, but Arabs are still being threatened Many arrests are done to young people not only young people because of really nothing they were doing on the social networks,” Amir Badran from the Jewish Arab Partnership Guard told Euronews.
"A ‘like’ that they put or a simple picture they put they’re immediately taken for terrorists for people in support of Hamas."
“Jewish people are very anxious, they fear," Itamar Avneri, from the Jewish Arab Partnership Guard added.
"People are also anxious and there’s tension between Jews and Arabs in Israel.
"It's very natural but we are trying to de-escalate, we are trying to de-escalate it and prevent violence to erupt."
An Israeli government official told Euronews: "Israel does monitor incitement and investigates every case".
For more watch Euronews' Shona Murray's report in the video above.