Separate but equal; where have we heard that before? Apartheid South Africa is no metaphor for anything else, but women of my generation and all those before were told over and over again that the sexes are different "but equal", as an excuse for excluding them from places they didn't belong: they should be doing "separate but equal" in the kitchen, bedroom and nursery. Whatever is segregated by diktat is rarely equal.

Universities once barred women altogether. Now they strive to be emblems of enlightenment, temples to reason, equality, free speech and freedom of thought. But it's not easy to balance conflicting freedoms. Universities UK, their representative body, has just published 40 pages of guidelines on External Speakers in Higher Education Institutions, wriggling and writhing over competing freedoms for women versus not causing religious offence: it ends up with excruciating nonsense.

Some students may want a "no platform" policy for speakers they find obnoxious – the BNP or members of unsavoury governments. Demonstrating opposition is a freedom, but banning or yelling down free expression within the law is a denial of freedom. However, Universities UK's guidelines give the sexist eccentricities of some religions priority over women's rights, by allowing religious speakers the right to demand women and men are segregated in the lecture hall.

Universities UK tells universities that "concerns to accommodate the wishes or beliefs of those opposed to segregation should not result in a religious group being prevented from having a debate in accordance with its belief system". If "imposing an unsegregated seating area in addition to the segregated areas contravenes the genuinely held religious beliefs of the group hosting the event, or those of the speaker, the institution should be mindful to ensure that the freedom of speech of the religious group or speaker is not curtailed unlawfully".

Good grief. The compromise is that women can't be put at the back: "The room can be segregated left and right, rather than front and back." Depressingly, the National Union of Students has endorsed this. What's wrong with "side by side" segregation? Just ask how that would look if universities allowed speakers to demand separation by race.

Muslim speakers demand segregation to make a very public point about their belief in women's "separate" role in the universe, one step behind a man, even in a place of learning. After all, as Maryam Namazie, head of the Council of Ex-Muslims of Britain, says, the speakers and the audience have all travelled there on trains and buses that are not segregated. Mosques and synagogues may hide women out of sight, but by agreeing not to "offend", the universities condone what they should confront.

The National Federation of Atheist, Humanist and Secularist Student Societies has found at least 40 cases within the last year where religious speakers demanded – and got – segregated university audiences. At the LSE freshers' fair, two atheist students were told to take off T-shirts showing Jesus and Mo holding up placards, saying "Stop drawing holy prophets in a disrespectful manner", and "Religion is not funny". The LSE student union pulled its literature off the stall and summoned security guards to force them to cover up their T-shirts: wearing them was an act of "harassment" that could "offend others".

Of course it might offend, but universities are supposed to be places that challenge beliefs. Atheist offenders will have their beliefs challenged too, by those who say Muslims are a persecuted minority who deserve protection from the dominant culture. What's more, Muslim students are more vulnerable, as the government asks universities to spy on them for signs of radical violence.

My own view is that religion is like any other opinion and deserves to be subjected to the same challenge or mockery as anyone's political views, with no special respect or forbearance. Universities are the anvils for hammering out these ideas, not for setting religious sensibilities above women's rights, and beyond challenge, trumping all other argument.

The power of religion in education is growing, not shrinking, even faster than under Tony Blair. The Al-Madinah free school in Derby that collapsed as "dysfunctional" a year after opening demanded all women staff wear headscarves, and segregated boys and girls in class and canteen – girls at the back. Michael Gove has sanctioned six new Islamic free schools. How could he not, when he has rapidly increased both the number and proportion of faith schools, to over a third, most of them Christian?

British Social Attitudes research finds 73% of respondents opposed to all religious state schools; yet once in place, faith schools are never dismantled by local mergers or closures. Recently it looked as if Archbishop Welby might open his schools to fair admissions in a recent interview, but the thought was withdrawn by a Lambeth Palace press release only hours later, recanting thus: "I fully support the current policy for schools to set their own admissions criteria, including the criterion of faith".

Next month the Fair Admissions Campaign publishes the most detailed social map so far showing how strongly religious selective schools have become a proxy for class. Muslim state schools also take many fewer free-school-meal pupils than the average for the neighbourhoods. Non-religious state schools with a high majority of ethnic minority pupils are caused mainly by local faith schools drawing away white children in the name of "faith". These 100% state-funded faith schools far outnumber grammar and private schools together. Andrew Copson, head of the British Humanist Association, says "they are easily the largest source of discrimination in our education system today". Universities, at least, should abide by secular neutrality.

• This article was amended on 26 November 2013 to clarify that a map showing the impact of religiously selective schools on socio-economic intakes will be published by the Fair Admissions Campaign.