Additionally, since version 1.1.0 (2019-09-05) also rewrites Twitter links to Nitter.Net. Reasoning is the same – and Nitter is to Twitter what Invidio.us is to YouTube.
How to select your preferred instance?
If you don't like the pre-configured one, you can simply change the videohost variable at the top of the script. Note that by editing the script inside Greasemonkey, the monkey will stop updating to preserve your changes – so you will then need to update the script manually.
v1.1.2 (2019-10-07): make it easier to switch to your favorite Invidious instance (just change a single variable); make invidious.snopyta.org the default
v1.1.1 (2019-09-06): do not exclude invidio.us but just ignore YT links there instead
v1.1.0 (2019-09-05): add Twitter2Nitter
v1.0.4 (2019-07-27): add update URL
v1.0.3 (26.07.2019): also deal with YT channels
v1.0.2 (20.03.2019): excluding Invidious itself from link rewriting so one can follow their YT links if needed