Cannot paste images from clipboard to Facebook in Safari unlike Google Chrome
This bug was fixed in Safari Technology Preview 51—basically early access to the next version of Safari—where you can paste images into Facebook there just like in Chrome. Hopefully that is enough to solve your problem! Video: https://youtu.be/ITyIWMyoyRk

Though the feature was broken in some later Safari Technology Preview builds, it was fixed for the public release of Safari 11.1 included in macOS 10.13.4 which was released on 29th March 2018.

—original answer—

If I do this:


Right/context click on a Tumblr image 
Choose "Copy Image Address"


Then both browsers paste the image URL into Facebook. No problems.

If I do this:


Right/context click on a Tumblr image 
Choose "Copy Image"


Then I get slightly different behaviour in browsers when pasting into Facebook. Chrome pastes the URL of the image, Safari posts the URL of the post/page containing the image. That's because Safari is much more thorough with what it copies to the clipboard in this instance, as it includes more alternate representations than Chrome. However both browsers still show an image in Facebook. No problems.


  As an aside, you can inspect what is on the clipboard using Finder > Edit > Show Clipboard, which shows the default format. For a more in-depth look, use Apple's Clipboard Viewer which shows extended information about the different representations stored on the clipboard. 


So I'm thinking that you are doing the Copy to clipboard in a different way? Maybe you can try using one of the above copy methods?