The cloud servers are down, apparently. Or, you did it wrong. If you sign out of your account when you go to Xbox Games Store, it will give you that error, and you can't go online until you dashboard.

I can still bring cars online just fine.

Yes you can, I just brought my modified Sultan from Campaign to Online.
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1. Go to GTA Online and create a Invite Only Session.

2. Take a random car off the street
and go inside LS Customs.

3. Once in press Start and go to Xbox Game Store and when you press A to confirm you want to go and leave GTA Online, plug out your ethernet cable or turn off your Wi-Fi and click A on both messages coming up.

4. Once in campaign mode take the car you want to the LS Customs and place it so the car is half way inside the LS Customs but it doesn't go in.
(That's what she said.)

5. Now sign back in to Xbox LIVE and go to GTA Online
and start a Invite Only Session.

Now you should see your car of choice half inside the LS Customs so just hop in that car and put the tracker
and insurance on it.

(Note that the car cant be any "too hot to modify"
car, as it then will give you that "error" as you are trying
to go in the LS Customs. You will need to do the "Insurance Glitch"
for super cars etc.)

How TO:

Hope this helped you out!