One of the reasons why this has become a big issue is that free speech is becoming a sensitive topic, with Waitrose being told to stop Daily Mail offers, Lego being told to stop giving away free things in The Daily Mail, advertisers being petitions to boycott the Daily Mail by people who don't read it, right wing activists being banned from universities and people calling on media outlets not to interview right wing people. There comes a point though when you have to start questioning who is the oppressive ones the people calling for a right wing government or the people trying to silence the people calling for a right wing government.
Like you, I share concerns about free speech now being a sensitive topic, as well as cases of where the right-wing get shut down or banned. Nevertheless, bigotry isn't exclusive to the far-left, it's just disguised a lot better on the far-right to the point where they can sometimes be seen as a voice of reason. It's how the alt-right got so popular; people were so disillusioned with the left that they thought they had someone to listen to. But for the most part I don't act on emotions, in fact I keep them away from decision-making. As such I could also end up seeing the alt-right views of identiterianism and white nationalism behind the deceptive nature, and though some have accused me of being alt-right, anybody who knows me would know it wasn't the case.
The question of the oppressed and the oppressor in a first world society is entirely subjective to where you are on the spectrum though. You might think that your voice is being censored because the Daily Mail is no longer being sold on trains or being offered at Waitrose, or Lego being told to stop giving away free things in it. On the contrary though, people who want to boycott and ban it think the Daily Mail is a tool of the oppressor who are out to divide and rule people it sees as scum (ie. Muslims and unemployed people). But me? Well, truth be told I don't wish to ban the Daily Mail because we cannot pick and choose who gets the right to free speech or freedom of the press, even if it is somewhat hateful. Free speech includes hate speech unfortunately.
Nevertheless, I don't expect anyone to get on board the platform of the Mail, which is extremely unreliable to the point where Wikipedia doesn't recognise it as a valid source, and can often be very deceptive and print deliberately provocative headlines to get readers and sales. A train company deciding they don't wish to sell it isn't censorship, and if a store makes the choice to stop selling it, it isn't censorship. The right to free speech gives you a platform to voice your opinion. It does not mean people have to listen or agree with you, as is the case on these Forums with many hating the Daily Mail. The argument of censorship is just the Daily Mail taking a victimhood mentality, and quite honestly I despise it when people do that. Unfortunately though it does seem to get a lot of attention, and sometimes even power.