AKA "nannyware", "Internet filtering", "content-control software", and "blocking software".
The least pernicious of these of programs act as automated Bluenose Bowdlerizers, intercepting all Net traffic and dynamically "blanking out" any text they are programmed to detect as "offensive". Naturally, such filters tend to be stupidly literal and are unable to understand context. Thus they are prone to falling face-first into the Scunthorpe Problem, and can end up censoring the most inoffensive webpages into incomprehensibility. And if the page so altered happens to be an input form, such as one used to create or revise wiki articles, the result can be the wholesale automated vandalization of the page's content. This is why evidence of censorware installed on a contributor's computer is one of the few things that can trigger an immediate temporary ban here at All The Tropes. However, if thoughtfully designed and implemented, simple text filtering can be relatively benign, with a low impact on the browsing experience. (It's still destructive of wiki content, though, and will still trigger an immediate tempban.)
The second level of functionality found in a large number of censorware programs is active filtering and blocking of entire websites. Theoretically, this is based solely on a determination that a site hosts content that is adult-themed, socially offensive, or illegal. However, as the website/organization Peacefire has made a point of demonstrating since 1996, a large number of censorware products quietly and rather comprehensively push a social/political agenda, almost universally that considered "right-wing" in the United States. Most famously, Peacefire has demonstrated that SurfWatch, Net Nanny, and CyberPatrol (among other programs) deliberately filter internet traffic to suppress political speech, prevent access to liberal and progressive content, and promote conservative and corporate causes. (Strangely, Peacefire often finds its own website blocked by censorware.)
Usually, second-stage censorware is not a problem for All The Tropes. Either we're blocked because someone connected to a filter's blacklist has decided we offend either their sensibilities or their politics (in which case you'll never get far enough to edit an article), or they let us through and we just have to deal with the first-level problem.
No real life examples, please; let's not advertise this software, okay?
- Subverted in Worm. Dragon, as moderator of the Parahuman Wiki, automatically censors Cauldron in such a way that makes evident the censorship is forced, while not succeeding at censoring anything. She does this as she is forced to enforce the spirit of the law, at the very least.
- Godblock isn't exactly fictional, but it is a wicked satire of and Take That at products like SurfWatch, Net Nanny, and CyberPatrol.