I just came back from a Birthright trip this summer. It was all girls, most of whom were young college age. Our trip started as an OU Free Spirit trip, but the organizer was switched to Israel Experience before the participants were selected.
All the food we had was kosher Mehadrin. Because it was a Shmitta year, we had special vegetables in some places. At the night in the Bedouin tent, a special mashgiach was sent earlier in the day to make sure we had food that was mehadrin kosher. For lunches we were told which places were good to eat.
I’ve heard that all the OU Free Spirit trips are run as orthodox trips, even if the participants aren’t.
If you are looking for a religious trip, try to find one run by JLIC.
We went to a few religious places, and few kevarim, and historical and nature hikes.