I made a resource pack that gives glass connected textures, but if I run the game without the mod installed, all glass has the "missing texture" colors. Is there a way to make a pack that doesn't break without the mod?

You can use the overrides folder property to have resources which are only applied when Fusion is installed. This can be used to just create a vanilla resource pack and then add or override certain files when Fusion is installed.
https://github.com/SuperMartijn642/Fusion/wiki/Optional-Fusion-Overwrites