I'm not saying all people making such arguments are making consistent arguments, but there's a consistent argument to be had that being forced to say (or write) something (say on a cake) and being forced to not say (or write) something are both compulsions in communication, and to be opposed to all compulsions in communication (to the positive or negative). I've heard several people argue that a cake shop should be compelled to sell a cake to a gay couple, but shouldn't be compelled to write two same-genedered names on it or compelled to craft a plastic figurine of two grooms or two brides for the top. I've heard it argued that if the gay couple wants "Susan and Jeff" and a little figurine of a bride and groom, or any other artistic expressions they'd do for a strait couple should be compellable, but the government shouldn't be able to compel artistic expressions or writing.
Now, I'd boycott the hell out of such an establishment, but as an abstract argument, I think compelled expression is a bad idea. It's really not that huge a step from compelled expression to re-education camps.
Twitter's service isn't that they write 140 character prose for you, and YouTube's service isn't that they create videos to your specification. It would be hypocritical to demand that YouTube be forced to create a custom video to your specifications (or a ghost writer forced to write a book for someone with whom they disagree) and yet the cake shop shouldn't be forced to write two same-gendered names on a cake. These people arguing against forced cake lettering aren't arguing for forced book creation or forced video creation.
Once again, refusing to make a gay wedding cake makes you a jerk and worthy of boycotting, but there is a consistent argument to be made simultaneously against forced expression and against forced silence.
