tumblr is not the government
It's a little worrying that not only the commentards can't tell the difference between a private company and the government, neither can the bloody company.
"Removing those authentic posts without your consent would encroach on your free speech"
No it won't. Because you (tumblr) are not the government, thus cannot impact anyones right to free speech*. Tumblr can (and does) remove, block and prohibit content *on it's service*, and should be able to do so. In fact, restricting tumblr's right to do so would be an infringement of free speech.
"This is beginning to look like censorship."
Private company removes content posted on private company's server. That's not censorship. If the feds had told tumblr, facebook et al to take the content down, then it could be. But you'll notice that the feds have a weird habit of strictly following the laws, which apparently is part of the recruitment process, along with shiny shoes, bad suits and the insertion of a stick up ones ass.
That tumblr et al are falling over themselves to self regulate rather than be regulated is another matter.
* perhaps with the use of a legal instrument like a NDA or an injunction