This is definitely not true. If you are Palestinian you don't have freedom of movement inside Palestine let alone freedom to enter Israel. They're not all permanently barred (gotta let them in so they can work for Israel) but they're not free.

You're also not able to live in peace in Palestine. Settlers regularly come in and drive people out. Food, water. medical supplies, and more are tightly controlled by Israel.

There are non Jews who are Israel citizens, including some Palestinian people, but that's a different story and those are not the people we're talking about.