Internet Accounts not showing Facebook, Twitter as options

As a result of your question, I have scoured various help files (MacOS Mojave, Photos, etc.). I see various references to sharing photos in Facebook, but it turns out they all reference the now-obsolete iPhoto app on the Mac.

So I tried an experiment. I opened iPhoto (which still exists in the Applications folder) and sure enough there is an option there to share via Facebook.

Be very careful if you choose this route, however, as there are incompatibilities between the iPhoto library and the Photos library. I strongly suggest you keep the Photos library as the primary housing place for your photos.

From what I've read Facebook and Twitter were removed from Mojave for security reasons.

Have you tried scrolling down and using “other account type?”