The two have very little to do with each other. What one could say is that higher level functional-like patterns are less idiomatic in Rust, because they abstract away from the low-level control that Rust also provides - which is why Rust chooses to provide, e.g. GAT's as a language feature as opposed to HKT's.

But functional programming is fully supported and lack of GC is not an issue, since you can use Rc<> and Arc<> where needed. (Support for 'pluggable' tracing Gc<> will probably be added at some point, but it will need local allocators, which are not a stable feature yet.)