First, I think we should clear some things up:
Recently an edit was proposed to one of my answers but before I got chance to review it, the edit was rejected by two moderators.
Firstly, it wasn't an action taken by Moderators, just regular users with the Review Suggested Edits Privilege, or >= 2000 rep. Moderators are users with a diamond (♦) next to their name, and are elected by the community.
As @Ash states in comments, Mods can automatically approve/reject edits without any other user input, which is not what happened here.
Suggested Edits and Review
...I find it very strange that moderators can approve or reject major edits to an answer without the author's consent.
This is a collaboratively edited site, and any content you provide here is posted under a Creative Commons license, meaning other users can alter and change parts of it at will. This does not require the author's consent, although we try to stick as close to the original author's intent as possible.
So what actually happened?
Checking the Review History logs, I can see this suggested edit on your post was rejected. Both users gave the same reason:
This edit deviates from the original intent of the post. Even edits that must make drastic changes should strive to preserve the goals of the post's owner.
This is a canned response but the reasoning is sound: both reviewers thought that the additions added too much new information to your post. And it really did: as I mentioned above, we try to stick to what the author intended the post to be (or what they originally said): clarifying meaning without adding additional info or 'putting words in their mouth'.
To answer your questions directly
1.When did this become a thing?
When Stack Overflow (and later, Stack Exchange) was initially created.
2. Why is this a thing?
Stack Exchange was built on the premise of community edited and vetted content. As I explained above.
3. Do any other Stack Exchange sites do it?
Yes, most do. (I'd say 'all do' but with so many sites in existence now I bet there's an exception that I'm not aware of).
4. Can I contest this if I want to?
There has been an addition just this week allowing authors to override community decisions on their own posts (and diamond moderators can override on any post):
- Any suggested edit to a question or answer that hasn't been edited after the edit was approved or rejected may be overridden.
- Only the author of the post that was edited and diamond moderators can override suggested edits.
- A suggested edit can only be overridden once.
When viewing a suggested edit that you can override, the "Next" button will be replaced with either "Approve" (if it was previously declined) or "Reject" (if it was previously approved):
Clicking this button will confirm the action, and then...
- ...if the edit was previously rejected, it will be marked Approved and the edit will be applied to the post.
- ...if the edit was previously approved, it will be marked Rejected and the previously-applied edit will be rolled back (complete with a comment in the revision history that describes what happened). If the editor earned +2 reputation for the edit, that will be retracted.
Once overridden, the edit affects the editor's suggested-edit stats accordingly. This allows moderators a tool to deal with the occasional bizarre form of abuse.