There is an issue with Realms excepting texture packs:

I have found that when attempting to upload/replace a realm with any texture pack, it fails to load at the end of the upload process. After the upload is complete and you play on the world the Texture pack is not loaded.

This was first noticed with the texture pack 'Pure BDCraft,' then was attempted with the SkyRim pack to no avail. Its matters not what system it is uploaded from it still will not work. I even Bought a 2nd Realm to see if there was an issue with the Realm itself and yet it still doesn't work.

This was first noted by a realm inhabitant after a approximately 1 week ago after getting a message that the Realms would be shutdown in 5 minutes for maintenance.

ISSUE RESOLVED in version 1.13