What would be a reason to scramble posts' dates during copy-and-paste (as Facebook recently started doing)?

Using the following clues, I'm fairly certain it's an unintended side effect of however they're implementing their internationalization. As you've noticed, this is not helpful, expected, or user-friendly in any way, so it almost certainly is an unpolished result of some implementation detail.

• As you mention, it doesn't happen when you're logged out, which would make sense, as they probably use a different method for determining how to render dates once they look up your full profile details. Before you're logged in, the method is probably just based on the time zone set in your browser by your OS or checking the general location of your IP. After logging in, it probably uses a dictionary of sorts to present the date in the official format for your exact region set in your profile.

• The example you provided is not actually the correct, localized date with extra characters mixed in, like you indicated in the question.
  StugsSpeptlogemnhrbermero 29cs atre t1c:ort08r hghedanrsPM
S ept em ber 29 at 1 : 08 PM
  "September 29 at 1:08 PM"
  September 29 at 1:08 PM = September 29 at 10:08 AM + 3 hours
  The fact that the jumbled mess *mostly* contains the same date, but only offset by a whole number of hours implies that the date representation is being calculated and rendered by the browser, based on the time zone it thinks you're in.

I did not check prior to today, but it works as expected for me this morning. I'm not sure if they've made a change to it's behavior since you opened this question, but I'd be curious to see if you still experience the same issue.