Speaking as the owner of a competitor site to pastebin, I've never heard so much trash in all my days.
Blacklist pastebin isn't the answer to any sort of problem.
Firstly you'll note wordpress is the actual issue here (as described) - if you want to be worried about something be worried about the insecurity of your actual app. What happened there might not be relevant to your problems (it's extremely likely it isn't).
Secondly what we're really talking about is the ability to both upload content and then fetch it from somewhere. Good luck with that particular game of whack-a-mole. What you're essentially saying is don't allow internet access of any sort. That might be a reality depending on the systems involved but there's no sensible half measures with this problem.