Could it be that this feature is broken? Let’s see (I’m pasting https://media.giphy.com/media/Lcn0yF1RcLANG/giphy.gif below):
Edit: okay, this is strange: discourse handles this gif in rather unpredictable ways. The first time I published this post, there was absolutely nothing in the rendered post. Then I added it to transparently mention the url I’m pasting and that produced a broken image placeholder the size of the actual image. The editor preview here on meta consistently shows a small broken image icon (not the size of the image).
On another site that I’m administering, the editor always shows the actual animated gif but the rendered post shows no trace of the image at all. Except when I rebuild the post-html, the url shows up as a link for a split second before it disappears again.
And finally, while I typed the above, the broken image placeholder in the post has disappeared from the rendered post. So at least after some time, the rendered posts look the same across sites, but still, something is wrong here.