Without disagreeing, I'd like to point out that if anyone can compel me to print their words on my platform, I no longer have the right to choose with whom I associate.
I see what you're saying and that's a great point, and perhaps I didn't make this clear, but I wasn't talking about the government enforcing a greater protection of free speech than it currently does. I'm only talking about whether a given individual can say they support free speech, and to what extent.
I would note that your freedom of association is already limited by the government if your platform is public. For instance, anti-discrimination laws are a pretty blatant violation of that right. I'm not 100% sure but I anti-discrimination might also cover speech, like if your platform says that people can't publish anything that is in the interest of black people (at the discretion of some officer of the company), is that legal? You might let black people publish stuff, and white people publish stuff, and make it a uniform ban (so black and white people both can't talk about things in the interest of black people), but is that legal? What if it turned out that the ban was affecting black people 90% of the time, so it was disproportionate based on race? I don't know.
Certainly even if it were legal, if your platform had a policy like that, nobody would agree that you're a strong supporter of free speech.
I think it's unfair to characterize a typical degree of support for the right to free speech as "not supporting it very much".
Perhaps I'm more optimistic of you, but I think most people support free speech outside of government interference. For instance, if you see a comment that you disagree with here on slashdot, do you mod it troll? Probably not. What do you think of people who do mod comments as troll if they just disagree with them? If you have a negative opinion of them, then you're demonstrating that you don't like their abuse of the moderation system to suppress speech. If you've ever shared those feelings, or commented "why was this modded troll?" then you've participated in exerting social pressure to protect free speech.
Again, if you go around modding comments troll just because you disagree with them, I don't think you can call yourself a strong supporter of free speech.