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YouTube Safety Mode is only managed through cookies rather than URL parameters. This is likely a decision made to stop people inadvertently having Safety Mode enabled by clicking on a random YouTube link. To force Safety Mode, proxies can directly manipulate the cookie headers of outgoing requests, for example on this Bluecoat article you can see the script ...


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Google has a reporting tool for objectionable content, such as websites and images. If websites aren't correctly filtered, you can submit them here.


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Use the Google Feedback tool as shown here and report to Google regarding the inoffensive image being filtered. I believe there is a mechanism on their side to check if an image is being filtered by SafeSearch.


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What I can suggest is to use the Google Feedback tool and report the image not being properly filtered by SafeSearch. I have the steps in this question.


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