10% of Tumblr is porn, right? And it's not amateur porn, or "oh hey I reblogged a butt." No, the vast majority of that 10% is one thing and one thing only: mirrored rips of full galleries from paysites. Illegal, copyright-infringing rips.
Basically, if Tumblr had any sort of scalable process to distinguish these from their other content, they'd just shut them down immediately. Using Tumblr just to bulk-rehost copyright-infringing images is 100% against their TOS, that much should be obvious.
Basically, Yahoo gave Tumblr some good advice here: if they don't want to fundamentally restrict their users from posting adult content, then it's all Tumblr can do (legally) to sweep these gallery-rip Tumblrs under the rug, so that you can only find them by seeing a reblog from them or by knowing their URL (which also, a lot of the time, means "by following a link from a porn subreddit.") It's not that they're adult; it's that they're in breach of copyright, and giving any public-facing path to them is the same as endorsing them (thus opening Yahoo to being sued for that infringement.)
This whole thing isn't about "OH NO A BUTT"; it's more for the same reason Mega's internal search won't show you "Adobe CS6 Master Suite [cw33t].rar", even though you could get that from them with the right URL. Hosting something is one thing; advertising it is another. Tumblr's emphasis on free speech is a mask for one thing here: they want safe harbor provisions to apply to them as far as this content goes, by not giving it any attention/promotion.
EDIT: I reposted this to Tumblr, expanded and phrased in a slightly more Tumblr-audience-targeted manner, explaining what safe-harbor provisions are and such. http://leviaul.tumblr.com/post/55886555106/you-guys