Hello Ken,
Thanks for that detailed steps. If Family safety web filtering is on, Youtube will enter Safe Mode automatically if you are not signed in on your Google account. If in case the settings for Youtube shows the Safe Mode is off but it is working properly
when doing a search, then this may be a user interface issue, and you will need to contact Youtube support for this.
As for the main issue of removing the Safety mode lock using another Google account if Family Safety is enabled, we would be needing log files to further investigate this issue.
Also, please verify the web browsers that you are using when performing the steps that you provided.
To gather the log files, please view my private message,
be sure that you are signed in to Microsoft Community and click the notification
which states that You have a private reply to this message. Click here to read it on our secure private message section or by clicking the
Private Messages tab.
We'll wait for your reply.
Regards.