Not sure I agree with the parent poster, but I think he/she is well aware of the distinction you're drawing, and says so up front. Certainly, legal freedom-of-speech protections don't require Kickstarter to host any particular content. But Kickstarter can still espouse freedom of speech as a value they try to uphold in their practices, even if they're under no legal obligation to do so. I think as more and more of our online interactions move to hosted platforms, we have to decide as a society whether or not we want the hosts of those platforms to police our speech. Those spaces can either be free-speech spaces or safe spaces, but probably not both, and there's a legitimate discussion about societal norms to be had about where we want that balance to fall, independent of this particular rather-icky example (and let's face it: most examples that bring this discussion to light are probably going to be icky).
How far do you take this? Kickstarter is a business and needs to make money.
Should it be acceptable for people to Kickstart escort businesses, "legal high" websites, or Amway pyramid schemes? All of those things are legal but are seen by the public as being slimy and taboo. Why would Kickstarter want to associate with these people?
Right, I'm not saying the all-free-speech route is the right answer for Kickstarter; in fact, in my personal opinion, it probably isn't. I'm just saying it's a reasonable question to ask, reasonable people can disagree about the answer, and the whole discussion is orthogonal to whether or not the first amendment obligates them to do anything in particular (since it doesn't).