It all depends on what you mean by "Wade" :) I mean it's an authoring tool, but can also be used as a simple framework,
If you want to use the editor to do everything (design your maps, write code, and all that), AND want to do this with other people using git, then you're right there isn't an obvious way yet (as of version 4). You will have to download your project from the editor every so often, unzip it in a local folder, reconcile your changes and then do a git commit / push. I agree this is not ideal, and we do have plans to make collaborative projects in the editor easier going forward.
However, you can also use wade like any other JS framework. Keep all your files in a local folder, use something like WebStorm or Sublime to write code, and use git normally like you would use it with any other JS framework. In that sense, wade is the same as any other library, you can easily integrate it with your own tools.
But when you do that, you can still use the wade editor to design your maps. Once you've created a map, simply download the map file (.wsc) from the editor, and save it to your local project directory, so it becomes part of your own git repo. Same thing for tilesets, characters, animations... you can design them in the editor and then save the relevant files in your local directory that is under source control.
I hope that makes sense, but feel free to ask more questions if you need assistance with setting that up.