Same thing for me on Xbox One. Beta worked fine since the beginning, got a 63(?) megabyte update this morning, played for an hour, left for lunch, came back and now when I start Destiny on the Xbox One is looks like it is about to install an update but then goes to the error code: zebra dialog box.
I've hard reset my Xbox One (something that is sadly often required to get Xbox One games to behave) various times to no avail, seems like it thinks it needs another update but that update doesn't exist.
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In addition to what was reported above, I should also mention my "INSTALLING DESTINY" screen shows me as being in a queue of 2484 people. It kinda seems like the update installation system is having a bad interaction with the server queues they are currently testing; eg. if you need an update but get put into a queue when connecting you just get bounced with a code: zebra error instead of either getting the update immediately and then going into the queue, or getting the update once your turn in the queue comes up.