No, at least not from Wikipedia's side (maybe some workplaces have such a rule). If you're editing on behalf of your employer, e.g. you're a paid PR person whose job includes editing Wikipedia, you're supposed to disclose that as a potential conflict of interest (you can still edit after disclosure). If you're just some person editing articles on their lunch break, there's no specific rule about it. However, if you're editing from a non-logged-in account, your IP address is attached to the edits, so third-party analysts can dig through the edits looking to see if they can correlate IP ranges with questionable edits, which is what's going on here.
In the discussion about edits from the Norwegian parliament that happened yesterday, it seemed like it was mostly perfectly innocuous edits: https://news.ycombinator.com/item?id=8024417
One thing to note about this is that this is just something new in the Wikimedia Terms of Use, imposed by the head office. Before the Wikimedia Foundation made the change to the terms, the self-governance mechanisms of English Wikipedia twice rejected this concept.
The addition to the legal Terms is new, but the English Wikipedia has long had a norm that you should disclose any conflicts of interest (paid or otherwise), and there have been community processes in place to warn people who appear to be failing to do so, at least when people with undeclared COIs made edits that raised enough eyebrows for someone to notice. You could maybe fly under the radar if you never made controversial changes, but warning templates like https://en.wikipedia.org/wiki/Template:Uw-coi and https://en.wikipedia.org/wiki/Template:COI go back to the early days of the encyclopedia. Some people who were found PR-scrubbing biographies for pay were also community-banned in the past, though those were case-by-case decisions.
While it was certainly not encouraged, you'll note that undisclosed COI was not actually banned, just discouraged. There was extensive and widely advertised discussion in November 2013 [1] about three anti-COI rules, all three of which were shot down. This is not the first time it has come up, and it had repeatedly been shut down.
As for the WikiPR incident, the fact that they were banned has less to do, I imagine, with the fact that they were paid than the fact that they were essentially vandalizing Wikipedia. If they were getting paid to write neutral, balanced, well-sourced articles, I'm sure no one would have cared.
The rule is that you should probably avoid exiting about your place of work, and that if you do then you should be transparant about it.
Most IP edits are good edits (most edits to WP are from IPs and they do most ofthe good edits) but there are some examples of people making unsuitable edits from their workplace.
No, nor is it necessarily a bad thing for politicians to monitor and even edit the Wiki, even their own pages. But, it is interesting to watch, and it definitely isn't appropriate for a politician or their staff to vandalize the Wiki pages of political rivals, or manipulate Wiki pages to advance a political message they're trying to sell.
Vandalism is vandalism, regardless where it comes from. There should be no need to discriminate editors on the basis of their profession or IP. Only the nature of their edits should matter.
