How can I disconnect a phone from Google's data backup service? Right now, I have two phones - my now-old Galaxy Nexus and my new Galaxy S5. I want to keep my Galaxy Nexus around as a Chromecast controller and (via wi-fi) streaming media device. As such, I want to remove apps that aren't useful to me for this purpose without affecting my Google backups that helped me set up my S5 quickly. However, when I go to uncheck the "Back up my data" option on the Backup &amp; reset menu, it says that disabling it will delete all my data from Google's servers. I don't want this, since my S5 should continue to use this service.

Is the fact that I have an S5 with this setting enabled sufficient to prevent my backup data from being wiped from Google's servers? If not, how I can unlink my Galaxy Nexus from this service? Or, alternatively, do I need to? The only thing that I'm trying to avoid is unnecessary syncing of apps and settings to a device that I want relatively free of apps.

In the event that I'm running on some false assumptions, I want the apps and settings on the S5 to be the ones restored on a new phone or following a reset. I effectively want the apps and settings on the GNex to be ignored as far as other devices are concerned.
You don't need to do anything. Every device using Google Backup with the same Google account keeps its own separate set of data. When you sign into your Google account for the first time after a factory-reset, the device will look through all the backup sets and try to pick the most recent one from the same device. It'll restore from that set of data, and use that to create a new backup set.

Only if you sign in on a completely new device that you haven't used before (not even before a factory-reset) will it choose a set from a different device: in that case, the most recently backed-up set.

So, you can leave your Galaxy Nexus backing up to its own set, and your Galaxy S5 backing up to its own set. If you factory-reset one of them, it'll restore the apps and data from the same device.

For a much more complete explanation of how Google Backup keeps track of different sets of backed-up data, see my answer to Google Backup: Multiple devices using the same account - what happens on Restore?