Starting on June 30, 2017, att.net customers will no longer be able to log in to their Yahoo and Tumblr accounts through email addresses with the following domains: att.net, ameritech.net, bellsouth.net, flash.net, nvbell.net, pacbell.net, prodigy.net, sbcglobal.net, snet.net, swbell.net, and wans.net.
If you’re affected, all you need to do to ensure continued access to your Tumblr account is to update your registered email address to something other than one of these addresses mentioned above.
The help article then goes on to tell people how to update their registered email address. Neither self-hosted WordPress, (or even WordPress.com), care what email address someone uses to log in, once that email address is associated with an account. And you can definitely create Tumblr-style sites with either platform. If you use self-hosted WordPress, you have even more options for adding features to your site thanks to plugins. There’s at least one plugin that will import all your Tumblr posts into your WordPress site, keeping them intact.
This really wasn’t a necessary move on the part of Tumblr. There’s no technical reason why someone’s email host should matter. A lot of these people have probably had these email addresses for a very long time, and to ask them to go get another one from somewhere like Gmail just so they can log into and use your service is wrong on every level.