This plugin blocks non-admin users from using inspect element, while still allowing access those with manage_options permission. The plugin also blocks some of the common keys(f12, ect.) and optionally can block right-clicks for non-admin users. Admins are unaffected by the plugin entirely. This plugin is also able to block users who open developer tools on another site, before visiting your site.
Version 3.0 update
This plugin is now fast and accurate, and should work on most browsers. This plugin can detect the browser console based on lag increased by opening the console. This detection is tough for a browser to prevent or get around. The detection runs fast, and has some resistance to lag spikes.
Lag detection does mean your site needs to have ok performance, but when testing it, I could play 10 of 10 youtube videos all at once without a false positive. During my tests, detection was still within the second I open dev tools, and successful if I go to the page with it already open. I tested this in chrome, firefox, and chromium. I also tested this on my somewhat slow website with tons of wordpress plugins installed (and the 10 videos at once test) without false positives.