Unfortunately I need to revisit my question from five years ago:
There is still no answer to this.
I'm using CopyQ as a clipboard manager now, and it works pretty well for most things.
From the CopyQ FAQ:
Unfortunately, this solution simply does not work. I create a document in LibreOffice, change the font and font size, copy from LibreOffice and paste into gmail and it keeps the same font and font size.
I never want this to happen. I want copy/paste to be plain text only at all times.
My workaround for the past five years has been to paste into vim, then copy again, which is obviously time consuming and frustrating.
What's the solution here? Something at the x.org level would be ideal, so it would be independent of clipboard manager (and would work without any clipboard manager).
I don't want any extra keyboard shortcuts either, just simple ctrl+c, ctrl+v as usual.