It comes down to content moderation. If a company begins to moderate content that travels through its network, it can be held liable and forced to remove things

It comes down to content moderation. If a company begins to moderate content that travels through its network, it can be held liable and forced to remove things that any entity or governmental body could disagree with. For example that means if the Republican Party was hosting on Cloudflare and the Democrat Party disagreed with the Republican Party, they could force Cloudflare to remove the Republican Party's websites from transiting their network. Another example is if the Washington Post and Fox news both went through Cloudflare, and Fox disagreed with the Washington Post they could force Cloudflare to remove the Washington Post. The moment you set the precedence it becomes an expectation -- by Cloudflare remaining neutral they can't be forced into that position.