Although in principle “safe” is a necessary precondition of most businesses, it’s being used in this case to mean “censorship of categories which have been poorly defined by people who think they’re obvious”.
As I grew up outside the USA and never lived in a culture of “freedom of speech is an inalienable right” (even after it became a right in the UK in 1998), I’ve always been comfortable with the principle of censorship. However, I do also understand the inherent danger of censorship, and that it makes certain social and political movements totally impossible. For example, one of the examples given in this story is that moderators are exposed to bestiality — an act which was legal until a few years ago in Germany when a moral panic about animal brothels caused the law to change. Just like a Bayesian trap, when it became illegal, any evidence that it shouldn’t be illegal automatically got zero credence and was no longer able to change the average person’s beliefs (if you are willing to continue to update your beliefs about that, good for you, but the ability is uncommon).
Now, I’m not going to argue for any particular prohibition policy positions on that or any other topic, but just the fact that “harm” isn’t defined in the UK proposal means that the censorship they call for is vulnerable to very large changes in short periods, and the nature of censorship means it’s likely to ratchet up rather than stay at any particular level. Not so much a “slippery slope”, more of a drunk walk/hill climber.
Of course, as I said before, I’m not a free-speech absolutist. I’d be very happy if we start with the basics like “don’t make death threats” and “take steps to prevent your users making death threats”. I just want it done properly, and one thing most people can agree on these days is that the UK government isn’t capable of doing anything properly right now.