From my test it looks like the only part that can have alternating background is the body. If you have a body part setup with alternating background and then change the body part to a different part it will leave the alternating background checked but it will be grayed out.
It turns out that the issue surfaced when I changed the script step from view as a list to view as a form.
When I changed the script step back to view as a list the problem went away.
Makes sense why this occurs.