The largest operators in any industry tend to support (and even lobby for) all kinds of costly regulations to create a moat around their business and cause the cost to enter said industry to be too steep for most.
It's interesting, because usually that lobbying is for something that generally helps people and can sometimes be seen as good legislation (such as tobacco regulation).
In this case, however, only harm is the outcome of removing the strengths provided by the first amendment.
The proposed benefit of the legislation that takes these companies into responsibility is, depending on what political camp you're in, either reducing hate speech on digital platforms or reducing arbitrary censorship.
Debatable on either front but pretty tangible in either case. It's not even clear what the first amendment means in this context because it can be evoked on either side, the freedom of private platforms to moderate as they see fit or the freedoms of users to speak on essential infrastructure.
When you selectively moderate, and exercise your first amendment as a platform, you are no longer simply a conduit - you are the conductor and you endorse all speech not removed.
Thus, all of these censor loving platforms should be held accountable.
Do you think you should be held accountable because you moderate the comment section of your blog, or Hackernews should be held accountable because they moderate their website according to their own standards?
This is the consequence of what you're proposing, a politically right or left leaning website say, simply by virtue of exercising freedom of association, would automatically become liable for content.
It seems pretty clear that this is unworkable and would, instantly, destroy the entire public internet.
There is a difference between moderation and selective moderation.
If a website moderates per pre-defined and agreed upon terms, then they should not be liable. If a website is going to moderate with a left-lean or right-lean, it should be up front about this agenda instead of selectively censoring or flagging comments.
Those definitions are fiction not founded by any law on the book. Nor in any jurisprudence - they are bullshit propaganda and are like citing "admirality law" by a sovereign citizen - proof of being actively incredibly wrong.
The courts have already ruled that even with right of way the government has no right to content standards on cable - now it magically is going to apply to non-excluding websites? Utter nonsense.