With the release of Firefox for Android 120 this method is no longer necessary

Since the release of Firefox 79 on Android in August of 2020 users have been unable to freely install Add-ons at will. Outlined below is a method to circumvent this, however this method only works for Firefox Nightly (or preferably Fennec F-Droid).
 

Step 1: Create a Firefox Account

In order to install Firefox Add-ons on Android you must create a custom Add-on collection which requires a Firefox Account. Create an account, and then follow Mozilla’s directions to create a collection.

 

Step 2: Download Fennec F-Droid

Download Fennec F-Droid using the F-Droid client. If you do not already have the F-Droid client you can install it from the F-Droid website. Alternatively, you can also employ this method using Firefox Nightly.

 

Step 3: Enable the debug menu

  • Open Fennec F-Droid and navigate to Settings
  • Scroll to the bottom and select About Fennec
  • Tap the Fennec logo 5 times
  • Return to Settings
  • Select Custom Add-on collection

 

Step 4: Add your custom Add-on collection

From https://addons.mozilla.org/en-US/firefox/collections/ click on the collection you created in Step 1. Your Collection owner (User ID) and Collection name appear in the URL https://addons.mozilla.org/en-US/firefox/collections/{Collection owner}/{Collection name}/. Enter each into the prompt, press OK and you can now install the Add-ons you have added to your collection.