Hmm; I'm not sure. I added it next to where the description is injected, in my theme (first image). But that seemed to take, just fine; inspecting the page, itself (after changes were saved), didn't seem to clobber the "rel='me'" part, any (second picture).
Just to make sure it all worked together, I've added a link to the Tumblr account to my Masto account and it's marked as verified. Maybe there's a type somewhere that caused Tumblr to not interpret it as valid HTML?