>"Surely there must be some way for advertisers to tell Google 'do not put our adverts on content provided by the following: ..."
Unless you are keeping very quiet about a massive break-through in Artificial Intelligence, the three dots at the end of your question can only be a list of specific providers.<
Either identifiable entities or meaningful categories should be manageable. There's enough money in the business to cover however much it costs to keep advertisers happy (or Google's business model is untenable). Advertisers may want to dissociate themselves from all sorts of content providers - particular political parties, religious groups, government agencies, competitors, themselves, entities from countries they don't trade in, etc; it needn't only be 'offensive' stuff (which is of course a subjective category, not a judgment that could be trusted to anyone else, human or AI). I'm sure some advertisers are delighted to be associated with content providers others might find 'offensive'.
The surprise is not that some advertisers object to some content, but that they hadn't already insisted on some mechanism to enforce their preferences - and instituted routine checks.