I don't even get the argument when it comes to universities- do they have to invite every single member of the population in to speak in order to avoid accusations of clamping down on free speech? What about Islamist jihadi preachers? Or the bloke ranting about the Kingdom is Coming down the park? Does he have to be given a platform? When is it ok to say "X is a nutcase and has nothing to add to our debate"?
As for newspapers, they are merchandise. Private companies can sell them or not sell them as suits them- and part of that will be whether they fit in with their image. And the same goes for public institutions. It is not a suppression of speech if cathedral gift shops do not feature Playboy.
Incidentally, my university staff room does not stock the Daily Mail. But then it doesn't stock the Daily Worker either. Basically, it only does the old-fashioned daily "broadsheets"- the Times, the Telegraph, the Guardian and the Independent (and the local paper, which is pretty right-wing). This is not to do with the suppression of free speech, but merely with an estimate of the kind of level of sophistication that their employees are likely to require in a newspaper.
Our Student Union shop does sell the Mail and the Express, but it's not something we can force them to do (or not to do) as a university: that is for the Union to decide. Given the number of foreign and immigrant students we cater for, I do think it's unfortunate that they should have to run the gauntlet of xenophobic headlines every time they enter the shop, but there is absolutely nothing I could do about that.