Toi: Birthright has a policy that you must stay with the group. It had nothing to do with the influence they might have had. They wouldn’t let him visit non-observant relatives either. When I went on Birthright, my family (chareidim) were able to come to the hotel in the evening to visit me.
On Motzei Shabbos, yes, they did take some of the group to a bar. For those who didn’t want to go to a bar, they had other options.