All the debugging steps you need are in the pinned post.
I just tried the http:// version vs https:// using
curl - the latter is successful, the former fails.
$ curl -L -v -A Twitterbot http://fb.me/3496PPgbo
* Trying 22.214.171.124...
* TCP_NODELAY set
* Connected to fb.me (126.96.36.199) port 80 (#0)
> GET /3496PPgbo HTTP/1.1
> Host: fb.me
> User-Agent: Twitterbot
> Accept: */*
< HTTP/1.1 400 Bad Request
< Content-Type: text/html
< X-FB-Debug: v8z+GoK/WQceIlC4UKxTSi1ui0/7J8xy2ny65uBTsOXel/pgvXCsNaXHQpR9qdHdZcot4soVy9rJDdbPqqW8tQ==
< Date: Fri, 05 May 2017 11:33:40 GMT
< Connection: keep-alive
< Content-Length: 0
* Curl_http_done: called premature == 0
* Connection #0 to host fb.me left intact
It is not clear whether that's a permanent change to that URL shortener to require or prefer https:// links, but either way this is not something that we can resolve on our side.