Rust is not a "write once, run anywhere" system in the ways that Java and the Web Platform are.
When we say that Rust is "cross platform", we are not making a very strong claim; we are only saying that Rust, being a much younger system than C and with only one known implementation, has not developed ecosystem fragmentation yet. Rust won't help you write code to run on multiple platforms (its system interfaces are at roughly the same level as the current-generation C++ standard libraries); however, it won't get in your way with "having to support several largely incompatible compilers" either.
(If you're looking for a "crossplatform gui library" that provides a native interface on "[Windows], Linux, Android, BSD", I think you're going to be disappointed regardless of language. The mobile user interface field seems quite fragmented.)