Epiphyt offers a very helpful and free WordPress plugin for blocking YouTube and Twitter embeds called Embed Privacy. The plugin shows an information screen instead of directly connecting to YouTube or Twitters server, visitors then can load the video manually:

And the best part: It also works in Gutenberg editor!

Plugin page: https://de.wordpress.org/plugins/embed-privacy/
Source: https://github.com/epiphyt/embed-privacy

Thanks very much to the devs for providing this as free and open source, really important for GDPR-compliance and for the broader WP community!

PS: If you are looking for a privacy / GDPR test tool, check out https://webbkoll.dataskydd.net/en.