We discussed this a bit on our Community Manager team call earlier... So I figured I'd share some notes.
First, some practical notes:
- Our imgur host URLs rely on randomly-generated filenames of 5 digits, each with one of 62 possible values - that puts the total number of potential image URLs somewhere north of 900 million.
- Imgur appears to be rather permissive in how it rate-limits requests. So it may be possible to scrape the entire set of images, although it'd probably take you weeks if not months to do it.
- Identifying PII within these images would also be challenging and likely time-consuming.
I'd say it's reasonably likely that someone has access to a bunch of sensitive information contained in i.stack.imgur images... Whether it's worth their time to extract it is debatable.
I wouldn't be overly concerned about leaking PII to random individuals via the choice of image host. It's not impossible that it could happen, or even particularly unlikely if you're, say, uploading full screenshots of a user page... But there are more realistic concerns in the specific context of your post. At the point where you're thinking about redacting specific parts of an image to keep it away from scrapers, you should stop and think about whether it even belongs in the hands of those you intended to share it with...
Leaking PII to specific individuals
An IP address - bereft of context - is not PII. A message to the effect of "user3829384298329 appeared from 220.127.116.11 at 3:51 on July 18th 2017" could be, so if nothing else be wary about the context you're including along with information like that.
But if you're revealing information about a specific user, their last-known IP address is probably the least of your worries; things like their real name, email or birthdate are problematic even if you're careful to exclude any other context.
And that stuff is still problematic even if you put it in text instead of an image.
If the person you're communicating with doesn't have access to the information you're providing them, then per the moderator agreement you should not be giving them that information - not in an image, not in text, not in public nor in private. You shouldn't be storing it on a "temporary" image host nor a private pastebin nor an access-controlled Google Doc or Trello card.
The security of the medium itself stops being relevant when the people you're intentionally giving access aren't supposed to have that access to begin with.
Err on the side of revealing as little private information as possible, ideally none at all. When necessary, you can share your observations of user behavior with moderators on other sites for the benefit of both sites... But you should rarely need to share the raw data from which those observations were derived. "These three users are connected" is both more useful and less dangerous than sharing raw access logs, regardless of whether those logs are in text or image form.