It seems to be possible but I can’t figure out how. I tried searching and was swamped by unrelated results. Little help?
Easiest things is to copy the URL from the Address bar and then post it the edit window on a line by itself.
When you post it, it should look like this in the edit window without the space between the slashes.
https:/ /www.youtube.com/watch?v=p_NS2H55dxI
Like this:
Note that there are currently some Discourse bugs that affect videos. See this thread for details along with workarounds:
That thread has 247 posts. Any hint as to which posts contain workarounds that work?
ETA: if your solution above works, then ignore this post!
Try writing the whole post in Notepad. Then copy and paste it into the message box and post it as fast as possible before a preview is generated:
If I go to a YouTube video, click share, and then copy the link, I can post it here. Then I add a back slash (/) and it embeds it in the post.
Where do you add the back slash?
After the URL that you copied from yt and pasted into your post
It would be something like:
https://www.youtube.com/watch?v=dYkDxgRYXcI
and instead you type
https://www.youtube.com/watch?v=dYkDxgRYXcI/
At the end of the copied youtube link, as stated above.
Well, but then Discourse writes
An error occurred. Please try again later. (Playback ID: PTSuR3_BOhkwrWcQ)
Learn More
when I click on the image in your post.
But if I click on the title of the YouTube post (upper left corner of the image: “Star Wars Holiday Special (Abridged)” in this case, post 5, yours has an error message so I no longer can read it) it opens a new window and links to the video in youTube. Then it works fine.
It didn’t use to be so complicated, but at least I found out that it still can work.
Well, shit, it works for me, so I don’t know anymore.
@Moriarty’s video worked fine for me, too.
Link + / worked.
That’s a forward slash.
D’oh!
Or a back-backslash?
I should add that there is a quirk to this. Once you post the embedded video, you can’t edit your post.
SLASH! Ah-ah! Saviour of the universe! 
If you get bit by this bug and need a post edited, just report the post and tell us what needs to change.
The selflessness of the SD mods knows absolutely no bounds.