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Safety tools are a proxy for the necessary social context needed to play a game safely; that is to say, safety tools are only useful in as much as they set expectations and that the group is able to adhere to or enforce them.

So when do you need these tools? Always. The trick is that they're not always something obvious like a sidebar talking about lines and veils, but rather the design choices you make to defuse and amplify certain tensions in play and your idea of what the play culture of the people playing your game looks like.

Xjere is absolutely right in mentioning that safety and accessibility tools often overlap, especially at community levels, because a safety tool is a kind of accessibility tool.