On the morning of 3 October, Chris Moos and Abhishek Phadnis put on joke T-shirts, of the kind students wear the world over, and went to man the Atheist, Secularist and Humanist Society stall at the London School of Economics freshers' fair. The bullying the university authorities visited upon them for the next 36 hours should provoke the most important free speech court case to hit British universities in years. It certainly deserves to.

Mention free speech and academia, and Pavlovian reactions kick in. The right complains, with justice, about politically correct restrictions on the ability to argue, often imposed by the rape apologists of the Socialist Workers party, who not only conceal crimes against women, but scream down the holders of contrary opinions. Again with justice, the left complains about the authoritarianism of university administrators and the police threatening rights to protest.

Earlier this month, the Guardian ran footage of a detective offering money to a student if he would spy on extremist groups such as the English Defence League and Unite Against Fascism (a front organisation for the SWP) and anti-fracking campaigners, UK Uncut and anyone involved in Cambridge student politics as well.

The Moos and Phadnis case cuts through the hubbub of charge and counter-charge. It shows that authoritarians of all stripes share the same vices, and not just because you know without needing to wait for their careers to "progress" that today's repressive student union politicians will be tomorrow's repressive human resources managers and Labour home secretaries.

The students wore Jesus and Mo T-shirts with designs by a wonderfully acid British cartoonist, who wisely never discloses his real name. Jesus and Mo are holding a banner that says: "Stop drawing holy prophets in a disrespectful manner NOW!" Mo also has a placard that reads: "Religion is NOT funny" and is saying: "If this doesn't work, I say we start BURNING stuff."

Are you offended? Really? Oh dear that's a pity, because if you cannot take a satirical reference to real religious censorship, your fragile sensibilities should be your problem and no one else's. Public authority should limit free speech only when it incites violence or unequivocally provokes direct and harmful discrimination against a vulnerable minority. The cartoon was doing neither.

The political hacks of LSE's student union, who are studying at a university that Sidney and Beatrice Webb founded in 1894 to promote "modern" education on "socialist lines," knew nothing of basic principles. They decided that the modern and socialist thing to do was silence freethinkers.

Student union officials told them to "lose the T-shirts" and pulled atheist literature from the stall. When the young atheists asked why they should submit to this impertinent demand, the hacks replied that the T-shirts were "of course, offensive". They did not say why. The LSE's security guards arrived and threatened to expel the atheists. Wearing the T-shirts was an act of "harassment" that could "offend others", they said. Surrounded by five of the university's goons, Chris Moos agreed to put a jacket over the offending T-shirt. This was not good enough for the LSE's head of security, because "prophet" was still visible above the jacket's neckline. That one word – "prophet" – was a horrendous insult to all right-thinking people, the LSE ruled. Chris zipped up his jacket all the way, but that still was not enough for the head of security.

"He told us he was going to leave two guards to monitor our behaviour," the atheists say in the formal complaint to the LSE's director. "These guards continued to follow us closely as we went in and out of the room throughout the remainder of the event. They intentionally intimidated and humiliated us in front of others."

The atheists are complaining about the behaviour of the university as well as the censorship of the student politicians, because – as you will have gathered – the supposedly leftwing student union and the establishment it is meant to fight aren't enemies but partners in repression, as the behaviour of the university's private police force shows.

If it were just the LSE, the affair would matter less. No one expects honourable conduct from an immoral institution, whose lecturers simpered like besotted lovers at Muammar Muhammad Gaddafi, while their masters pocketed Libyan money. The university either does not know about or wilfully ignores the need to condemn religious prejudice, which kills and blights the lives of millions, while always permitting uninhibited criticism of religious leaders and dogmas, in whose name millions more are killed or have their lives blighted.

The National Secular Society offered to fund legal advice, which has now been secured by the Federation of Atheist, Humanist and Secular Student Societies and the British Humanist Association, to launch a test case against the LSE because censorship is so common. The National Union of Students, for instance, banned the feminist campaigner Julie Bindel from speaking at British universities because she had written a trite and unpleasant article about transsexuals in 2004, for which she apologised. That Bindel helped rapists' victims rather than covered up their crimes did her cause no good. When student politicians at last allowed her to talk to the audiences they corral, Bindel had to pull out of addressing a meeting at Manchester University after receiving death and rape threats. Naturally, university administrators have taken advantage of the oppressive climate. Leftwing activists have learned that oppression cuts both ways. Universities call in police-dog handlers to round up students protesting against the privatisation of campus services or course closures.

On the "occupy" left and establishment right, hardly anyone thinks that the ideal university education should be offensive; that the young ought to have their beliefs challenged in the most robust manner imaginable. If their beliefs stand up to the challenge, they will be strengthened. If not, they should change them. If students cannot take the smallest of challenges without running to authority with hot tears rolling down their cheeks, they shouldn't be at university in the first place.

Instead of producing confident students who can handle any argument you throw at them, universities are a production line for cowed conformists. Instead of being free spaces where ideas can be debated without restraint, universities have become like the private and public bureaucracies the young will go on to join: speak out of turn, or even wear the wrong T-shirt, and the bosses will make you suffer.

• This article was amended on 29 November 2013. An earlier version said that the National Secular Society has taken counsel's opinion and is appealing for funds to launch the test case against the LSE. The National Federation of Atheist, Humanist and Secular Student Societies has asked us to make clear that the National Secular Society has supported the LSE Atheist Secularist and Humanist society through public statements and have been included in discussions on drafting the LSE society's statements. However, it is the National Federation of Atheist, Humanist and Secular Student Societies and the British Humanist Association who are providing legal assistance to LSE ASH, and have secured it on a pro-bono basis.