Can keychain support be turned off?

You can remove iCloud keychain from apple's servers:

Use these steps if you're using OS X Mavericks v10.9 or later:

1. Choose Apple () menu > System Preferences. Click iCloud, then click Account details.
2. Deselect “Allow approving using security code."
3. Go to each of your devices that are using iCloud Keychain and turn iCloud Keychain off.

After you complete these steps, your keychain data will remain locally on your devices, but changes to your keychain information won't push to your other devices or the cloud unless you turn iCloud Keychain back on. If you want keychain data to push to all of your devices, but not to the cloud, turn on iCloud Keychain on each device, but skip the step to create an iCloud Security Code.

I finally got so sick of all the pop ups and demands that I just somehow manage to disable iCloud and delete the Keychain. Did not make any difference to the annoying little gremlins though, because some remnant of it will always remain in the system. So, now I just get keychain pop ups telling me there is no keychain for whatever it was trying to access. Progress? Depends on how many times one has to click to make pop ups go away

PS This is, of course, all with the infamous El Capitan

Open Finder

In the menu bar select Go then Go to Folder

Go to: ~/Library/Keychains

Move all contents, including sub folders, to the trash.

Do not empty the trash

Restart the computer

A new keychain will be created

Passwords for iCloud, mail accounts, and other internet accounts can be entered into the new keychain.

Keychain itself is part of the operating system and is required, it cannot be turned off. iCloud Keychain is just so keychain data can be synced between multiple computers and devices.