Halfway through a 10-day tour in Israel, Risa Nagel had a decision to make.

The 25-year-old grant writer from Seattle had hiked the hills of Galilee and wandered the ancient market in Jerusalem. But then some of the friends she had just met told her they were planning to walk off the tour to visit a Palestinian family, an act of protest that was bound to cause pain and controversy.

“We will be able to see for ourselves what’s going on,” one of them told her. “Do you want to come?”

Ms. Nagel agonized. The next day, after the group held a moment of silence at the Western Wall, her friends announced that they were walking off. She followed them.

Over nearly two decades, a nonprofit organization called Birthright Israel has given nearly 700,000 young Jews an all-expense-paid trip to Israel, an effort to bolster a distinct Jewish identity and forge an emotional connection to Israel. The trips, which are partly funded by the Israeli government, have become a rite of passage for American Jews. Nearly 33,000 are set to travel this summer.