You're all welcome! I'm glad you can now use Tumblr on mobile without having to worry about huge chunks of your data disappearing, haha.

I was too at my wit's end with this problem - Tumblr is my most used social network and the tumblr app is not only useless but consumes far too much data for my plan as opposed to Opera Mini. But I found a fix!

Go into the settings of Opera Mini and toggle Single Column view to "on". The Tumblr homepage will look outdated and frankly horrific next compared to how it appears when single column view is disabled, but after login you can change back and all will be fine. Then, enter your email and password in the two top boxes and click "submit" rather than "log in". A captcha test may appear, but that's irrelevant, don't bother with answering it. After "submit" is clicked, you should be taken to a very outdated looking version of your dashboard, and then you can toggle off single column view in settings and the page should automatically refresh to normal view.

Tumblr on Opera Mini isn't perfect and the reblog button is far from trustworthy, but it's better than not being able to log in at all.

My instructions of what to do may be a little off concerning what to do when the login screen is reached because I haven't logged out of Tumblr to go back in again (just in case it was a one off and it'll never work again) but I hope this helps.