It's far from easy in the case of Firefox [0], and the last time I tried, some .mozilla.com domains would still get pinged. Chromium doesn't even have an official guide. The only options I found to be reliable are source-level patches, i.e. ungoogled-chromium and LibreWolf.

Note that LibreWolf still leaves some of the stuff on for you to manually disable (dom.push.connection.enabled, extension updates).

[0] https://support.mozilla.org/en-US/kb/how-stop-firefox-making...