The argument was that when said company becomes a "commons square" by being almost monopolistic (like YouTube and Twitter), should they then have some duty to not censor? Or at least do it transparently? Or at least not collude with government agencies on what gets censored?
That some services are large and show monopolistic tendencies is an anti-trust issue and not a 1A issue. Arguing that companies that fulfills criteria X shouldn't have 1A rights is the road to some really fucked up things like the government explicitly tampering with the 1A in certain scenarios, and then the 1A become this fluid morass of shit that won't matter very much in the end. And in regards to colluding, no such things happened. Was there some improper behavior exhibited, sure - but most of the stuff that went on is on public record. The government in its capacity as a governing body has the right to communicate with private entities and suggest actions. The only time this matters is if the private entities doesn't have a choice but to follow the "suggestions" or suffer consequences. An example of such behavior is a politician saying "If you don't stop censoring "political group A" we will remove section 230 protections for you!" - that is a blatant example of someone trying to abridge the 1A by threatening the private entity with repercussions if they don't what the politician wants. A politician saying "This content posted by this person doesn't adhere to your community guidelines." is perfectly fine, but if it was followed up with "Or else!" it runs into the 1A.
And the word "publish" (your Freudian slip) implies they are a publisher, not just a carrier, and then should be held liable for postings.... and yet they are not, due to section 230.
If you actually read what the authors of section 230 said about it is that all internet services that hosts 3rd party speech are publishers but they aren't legally treated as such when they publish 3rd party speech. This changes if they choose what is published beforehand (editorial selection of content), then they become a publisher in the legal sense too (although there are some minor caveats to that).
Many people miss this distinction which is why when those who understands this says "they aren't publishers" they are entirely correct in the legal sense. Context matters and especially so when it concerns legal definitions and scopes.
It isn't quite as cut and dry as it would seem. They want it both ways- to claim they are open and free commons and thus should be exempt from liability, and yet also want to censor, demonetize, shadow-ban, blacklist, disclaim, discriminate, downlist, and lots of other "shaping" and interference (outside of user control and often awareness), like a publisher would do.
It's very cut and dry, legally everyone is responsible for their own speech and everyone has the choice of not being forcibly associated with someone else - all per the 1A. The whole "they want it both ways" are certainly a red herring and they certainly aren't "open and free commons", that's some made up shit. They welcome anyone that agrees to their TOS/rules which usually say that the owners can take any action they want within reason to run their service as they want, ie they can remove, hide, promote, downlist, demonitize, monitize etc any 3rd party content at will. If you don't like what a service is doing, vote with your feet.
The problem with pushing the idea that an internet service should always be treated as publisher even for 3rd party speech, means that only the big companies that hosts 3d party speech will survive in a fashion, because they have lawyers to spare. The rest will either shutter, disallow any 3rd party content or only allow pre-vetted content through (total editorial control). It's the road to the internet being a read-only pipe of content, which big companies and politicians would love - not more dissent being voiced.