... yes? We would say that.
That's exactly how we draw the line now. For example, nobody would demand a stadium offer naming rights to the KKK, but the state of Georgia had to allow that organization to "adopt a highway" under its charity-for-recognition program (https://www.cnn.com/2016/07/05/us/georgia-kkk-adopt-a-highwa...).
Ultimately, there is no uncontested free speech right in private conduct. If I am exercising a speech right to (say) rent a billboard for an advertisement, then the owner of that billboard is also exercising one if they give me a discount because I'm advertising kittens for adoption.
Once the government gets involved, however, it is often acting with the force of law. That is where we deem free speech rights to be sancrosanct.