Mixer on the Xbox can stream natively to Mixer and can even add a facecam via USB. It's not as flexible as OBS, of course, but it does work. In fact, if you have access to a second Microsoft account, you can stream natively out of the Xbox to Mixer, and then use the browser source in OBS on your Mac to import that stream and then restream it out to another Mixer account or other services.
I regularly use Mixer this way because I have a let's play team that is spread out over the world-- raw game footage gets streamed to Mixer so all our participants can watch, and then our audio chat is added to that footage and sent out again to other services.