But companies don't have the right to refuse baking a gay cake? What a messed up world we live in.
I don't think a public company can ban someone unless they are breaking the law on premises?
Companies do have the right and a guy actually beat a gay couple in court who tried making him bake a cake which violated his religious beliefs. I commend the verdict, myself!
The thing with that ruling was that the court found that the State was prejudiced against the guy baking the cake in the State's ruling. If the State had not been prejudiced against the baker, the ruling could easily have gone the other way. Give it time, another court case will come along and the ruling, this time, might not be the same.
"Social media companies are adamant that no such bias exists"
"some algorithms did cause lower prominence of certain individuals, but that the mistake has been remedied"
Uhh... So, openly lying? At least they are honest. Oh wait, not...
This needs to be for all sites, not just social media. Blocking people from this on any site is a hit against free speech. It is effectively walking up to someone on the street and putting duct tape over their mouth. I agree some probably need it.

Although you are free to avoid it.
Because their algorithm was causing a lowered prominence of certain individuals is not evidence that it was deliberate, and, therefore, not evidence that they were lying. All computer algorithms must have conditions on which they act. Something like these algorithms are far trickier to code than others. These algorithms are along the lines of AI.
Wow I googled if you could make racists billboards out of curiosity and you can... Anyways if you are using a platform like Techspot you have to abide by their rules. Social media is no different. If you disagree with their rules don't use it. Make or find one that caters to what your about.
There are rules that go beyond that. From what I have seen, most supporters of the First Amendment seem to believe that the FA means that you can say anything you like at any time you like in any context that you like. That is not at all true and there are exceptions. The FA does not cover inciting violence in cases where violence is likely to occur and SCOTUS has ruled as such. Here's a case from Ohio that cites the SCOTUS ruling and makes a point about the determination of whether such violence is likely to occur -
https://www.law.cornell.edu/supremecourt/text/395/444 In this particular case, SCOTUS ruled 8-0 for the group in question because they said that in this case, the suggested violence was not a clear and present danger, and this is likely why you can publish a racist billboard.
There is good coverage of exceptions to the FA at Wikipedia -
https://en.wikipedia.org/wiki/United_States_free_speech_exceptions
It certainly is true that private companies have the right to set terms for access to their services.
However, if there is a systematic and pervasive bias against legitimate views by the majority of major web platforms, that would have an adverse effect on public debate. So circumstances could exist under which an investigation of this type would be legitimate.
That this does not appear to be the case at this time, with Trump equating entirely appropriate sanctions against racists as an attack on him, Republicans, and conservatives, may well be true, but it is separate from the general issue of whether, in principle, it is legitimate for the government to look into the thing it is claiming to be looking into now.
There does not, as you note, appear to be a systematic and pervasive bias against the legitimate views of the majority.
As the old saying goes, the squeaky wheel gets the grease. To me, those on the extreme ends of the spectrum are making the most noise and getting the most publicity.
Those near those ends then latch onto these cases and overgeneralize by saying ALL on right or ALL on the left are being suppressed - which is not the case.
If ALL on either "side" were being suppressed by any web site, that would be absolute evidence of that systematic and pervasive bias exists; as I see it, however, those with the loudest mouths are the ones that seem to think they are being suppressed. As I see it, the behavior that Twitter is using to ban Alex Jones is covered in one of the exceptions to the FA as discussed in the Wikipedia link above - look for "Fighting Words".
Whether US citizens of any political flavor like it or not, SCOTUS has placed limits on free speech within the context of the FA.