Exporting Godot projects using godot-rust is a 2 steps process:

If the target you are exporting to is the same as the one you are developping on, the export is straightforward, however when cross-compiling (eg: exporting for a mobile platform, or building from a Docker image on a CI) you need to correctly set up a cross-compiler for the target platform. Rust does this very well, so provided you only write Rust code, cross-compiling is easy. However to build gdnative-sys you need a working C/C++ cross compiler with, among other things, the correct headers and linker.

How to set up such a cross-compiler depends on the source and the target platform.