There are couple of WP plugins built on JavaScript techniques to protect the source code of the page and disable image saving via right-click. I will mention two of them, just because they are still being supported and updated from time to time, other similar plugins haven’t been updated for the last couple of years now.
No Right Click Images Plugin
The good thing about ‘No Right Click’ is that the product disables image download, still allowing users to apply other options of the right click.
The plugin is absolutely free. It also includes ‘Prevent Drag and Drop’ option. Authors also added a nice feature to the settings, giving logged users ability to save images, yet keeping the surfers blocked from saving ability.
Good to know that Images uploaded via the WordPress Media uploader will open in a window if clicked. They are not protected, so this plugin allows to indicate that there should be no action if the image is clicked.
WP Content Copy Protection & No Right Click
This plugin has more options including functions to disable CTRL+C, CTRL+A, CTRL+V and other button combinations, allowing to protect not only screenshot captions but also texts from being copied. The same options are equal for Mac users.
The Pro version which costs 29$, includes pop-up alert messages when user hit the right click button. Also Home page or single posts protection can be selected separately.
Of course there are some techniques with server-side scripting you can use instead of these plugins to hide direct source or URL to the image. Browsers can only see what you want them to see.