I see. Preventing access to
classes of behaviour is a harder problem. Reentrancy (single threaded - such as mutual recursion) must be really hard to detect with certainty other than at runtime, for example. In a multi threaded context it's obviously even harder.
Classifying functions into more categories like "interruptible", "uninterruptible" seems doable with enough language support. It doesn't look to far from what e.g. Rust and C# does with "unsafe", i.e. a status of functions that bubbles up so that your function may be tainted as unsafe by calling unsafe functions. If the number of classifications of functions is small as is the case with unsafe/safe, or uninterruptible/interruptible then it would seem possible to sort this out via compiler support and keywords for example. So for example a signal handler is then an uninterruptible function. It's a compiler error to call even indirectly, or dynamically dispatch to interruptible functions.
For any type of safety, dynamic dispatch obviously needs to be done in a type safe manner, so no pointer arithmetic/function pointer invocation can be allowed. Doing so would make the called code be assumed to be the worst of all categories: unsafe, interruptible etc). This is how unsafe/safe works too.
So while it's cumbersome I'm sure it would be possible to achieve at least to some extent, given an expressive enough language and a clever enough compiler.