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Did you try disconnecting the Internet and then booting each disc? I don't own either of the Halo releases on Xbox One so I don't know if they're playable without the patches (I recall Halo MCC's campaigns supposedly being completely playable without any patches); however, plenty of other Xbox One titles like Dead Rising 3 and Sunset Overdrive are playable offline without the patches.

If you want to play online or see achievements pop in real time, though, you're going to have to download all of the patches.