This actually turns the idea of free speech on its head: If your actions (which should be considered speech) are forced to support others' speech, then that's not free speech. That's forced speech. Most individuals, and non-government funded institutions, should be free to choose which speech they actively support, and which speech they simply ignore.
Too often, proponents of free speech are actually promoting forced speech. They claim that not actively distributing, repeating, or hosting certain speech "suppresses" that speech, when, in fact, the lack of support is simply just that -- a lack of support. To force the support/disemmination of speech is antithetical to free speech.