Does anyone know how to pass a variable from automator to Applescript?

You are providing rsync with an HFS path and not a POSIX path, so it just goes berserk.

on run {input, parameters}

	repeat with afile in input
		set unix_path to (POSIX path of afile) as text
		# do shell script "echo " & unix_path & " >> ~/Desktop/logme.txt"
		do shell script "rsync -R " & unix_path & space & "/Volumes/RAID_1/_Shows/_Staging"
	end repeat
	return input

end run

Of course, if you are just doing shell stuff and have no specific AppleScript coding requirement, you could use a Run Shell Script action instead:

When you drop a series of files/folders on an Automator application using Run AppleScript, you treat and process the input variable just as you would a list of aliases:

This example would append each dropped HFS file path to the logme.txt file on the Desktop.

You are welcome.

On macOS Catalina and later, the default shell is now zsh which Apple plans to continue supporting due to its MIT license. The near prehistoric Bash 3.2.57 shell remains available for those that prefer it, though unsupported by Apple. Newer versions (e.g. v5) of the Bash shell (and syntax examples that you will likely see in Google searches) are not installed by Apple due to its GNU licensing (GPL) v3 restrictions that Apple does not agree too.

You can find more information on the use of the zsh shell here.