It’s nothing to do with the plugin itself – it’s Facebook & Scheduled Posts.
Thanks to a lot of random Googling, I found an article that described the issue well here: https://www.passwordincorrect.com/issue-with-sharing-wordpress-posts-to-facebook/ that had a very timely comment(expand full comment for complete code) by a kind soul who has also made the code available here: https://gist.github.com/leandersikma/1c5507d2cbd29e580e94 (just today, it looks like!)
I put the code from the comment in the theme’s functions.php file and next scheduled post linked to Facebook with no 404.
I don’t work on the site day to day, but I also haven’t heard about this issue again since I applied the fix from the commenter, so I’m assuming that is is still doing the job.
Hope it works for you, too.
