>that the Republican Party got rolled back in the 80s
Yes, this is true.
>ruled unconstitutional iirc
You've completely misremembered/misunderstood this part though. The Fairness Doctrine was revoked by Reagan/Nixon-appointed FCC ruling, an action which was actually opposed fairly strongly by Congress at the time (just not enough to get a veto-proof majority over Reagan to codify the Fairness Doctrine into law). The FCC's ruling was upheld when it was appealed in the courts but not on any grounds touching the Constitution, it was merely decided that it was the FCC's jurisdiction as the law existed and up to Congress to pass something specific (which could then in turn be challenged) if it wished to not delegate that.
However previous rulings on the fairness doctrine indicated it was Constitutional. The First Amendment is the most powerful free speech protection in the world, and "oh but exceptions" is constantly overused in the press and general discourse. However laws can be passed that will survive strict scrutiny in specific cases, where there is a "compelling public interest" and the law is as narrowly tailored as possible and there are no other ways to do it. In the case of public broadcasting, there is in fact a limited amount of usable electromagnetic spectrum available. That's not a matter of human opinion but of plain physics. Broadcasters aren't and weren't operating in some wide open venue, they are using government granted monopolies on regulated slices of spectrum which itself is public property. It is not therefore against the First Amendment necessarily to craft limited, specific rules governing that which would be unconstitutional if done for print.
Or for that matter for the Internet. Which is where the current Republican arguments really go off the tracks. The interest of the rules that applied to broadcast (or even possibly cable TV if it's done using public rights of way) does not exist for general dumb information pipes anymore then it does for print (or even less). Merely being a bigger and more popular private newspaper has absolutely nothing legally to do with any "fairness" requirements, the measure is what sort of natural physics obstacles exist to them starting their own newspaper in a vacuum, not whether it succeeds. The Web is decentralized just fine from the start, anyone can throw up their own server and put up what they wish, they are not inherently entitled to force anyone else to serve as a loudspeaker.
The only areas I can see where things could get problematic is where companies have created significant and exclusive walled gardens or where physical infrastructure is involved. So Apple on iOS could (and should, IMO) be more of a question. But not on their website or the Mac, including in the MAS. Google in general should have zero obligation, but Google Fiber or maybe Play Store (weaker case then Apple) could be exceptions. Etc.
But right now what a lot of these conservative actors are engaging in is a one-sided perversion of Freedom of Speech and Association: they're claiming that only they get that right. But in reality and legally everyone else they interact with does too! Duh. And that in turn means that everyone else they deal with by default has the right to think their ideas are stupid and worthy of scorn and social ostracism and so forth. That's a feature not a bug, it's the whole point of Free Speech! The point is to work towards good ideas and make sure that over the long term it's possible for those to get out through hard work and determination and evidence and good argumentation, not that all ideas are worthy of respect.