So you are future-ready and have full IPv6 connectivity perhapps in a dual-stack with IPv4. And some of the picture on tumblr won't load. The browser will keep spinning but never show the image. 

IPv6 is the cause of the connection issues, as Tumblr is not IPv6 ready. Tumblr support says: 

Hello, Sorry, but IPv6 connectivity isn’t supported on Tumblr at this time. We’ll share your desire for this feature with the rest of our team. Thanks for your curiosity, and let us know if you have any other questions

Sadly nobody told Tumblr's Content Delivery Networks (CDNs) that Tumblr is too 90s for IPv6 and at least two of their CDNs, namely Highwinds and EdgeCast, are IPv6 capable and announce their IPv6 addresses and accept IPv6 connections. And these IPv6 connection hang forever and will never return the requested content. Using the same address and forcing IPv4 will return the requested. 

I tested this with curl and see that with IPv6 the connection is established, the headers are sent, but then no content is returned probably as the CDN server is waiting for information from tumblr. With IPv4 forced everything works, the connection gets established, HTTP headers are sent and received followed by the content. If the IPv6 connection would be rejected outright, the browser (at least Chrome) would try the IPv4 connection and everything would work.

In my case I needed to null-route the IPv6 networks 2606:2800::/32 and 2001:4de0::/32 and tumblr works better.