Here's the info on how to turn off "Safe Mode":

https://tumblr.zendesk.com/hc/en-us/articles/231885248-Sensitive-content

As for blogs only show up in your sidebar the first step is to click on the blog's icon and see if it will open in a new tab. If that doesn't work it apparently has something to do with privacy settings allowing only logged in users. I'm not sure how that interacts with Tumblr's new policy making some blogs only available to logged in users.

Hey Matt - I established a Tumblr 'account' a couple of weeks ago anticipating this. Can I turn safe mode off? And do I have to occasionally do something so they don't kill the account - like posting a random picture? Just one more - when I look at a Tumblr page now that requires a login, it shows up in the right hand side of the page instead of full screen - is there a way to fix that?
Sorry to bother you - but you are the reason I first looked at Tumblr several years ago. The best thing ever to happen to people who happen to like to look at naked men!