Solaris and Karma utilze MaterialX through UsdMaterialX, a plugin that allows USD to import MaterialX shaders. Houdini lets you build MaterialX materials in VOPs and translate them into a UsdShade prims automatically. While there is a script that can convert VOP nodes into .mtlx files on disk, the primary workflow Solaris supports, is MaterialX nodes encoded as USD prims. Solaris can reference MaterialX looks defined in .mtlx files on disk, but support for writing to .mtlx files is much more limited.
If you need to export .mtlx you could look into authoring MaterialX in the standalone QuiltiX editor: https://prism-pipeline.com/quiltix/ [prism-pipeline.com]. Apparently you can even use Karma as a Hydra delegate.