No they could not. Rusts standard library heavily uses dynamic memory allocation and panics, for example. MISRA C:2025 Addendum 6 covers MISRA rules that still apply to Rust, as an example of how one would restrict Rust in safety-critical contexts.
In safety critical contexts, you're not usually using the standard library. Or at least, you're using core, not alloc or std.
Panics can still exist, of course, but depending on the system design you probably don't want them either, which is a bit more difficult to remove but not the end of the world.
I hadn't seen that addendum though yet, that's very cool!
If there is a backdoor in an open-source system, and people know about it, then they will organize independently to patch it out. So it will be ineffective to the extent that the technology allows reprogrammability.
The only way you can beat it, as a governement trying to insert a backdoor, is through use of tivoization or some other technology that clinches control during manufacturing or other centralization weak points around economies of scale that the re-programmers don't have.