First, I just want to highlight that reason cell site simulators (the more general term for StingRays/IMSI-catchers) exist is because cell phones cannot authenticate all messages coming from cell towers. I'm seeing some vague comments about "a lack of encryption", but it's primarily more of an authentication issue.
You can read more about why it's primarily an authentication issue + how some of the relevant types of cell network attacks work in this technical post I wrote for EFF: https://www.eff.org/wp/gotta-catch-em-all-understanding-how-...
There are some interesting proposals for fixing this lack of authentication using a certificate-based PKI system, the most promising being this paper from Purdue: https://relentless-warrior.github.io/index.php/publications/.... This solution is very far from production-ready, but it's a much-needed step in the right direction.