Are you free to think whatever you like? Of course you are. There are no thought police, though the paranoid right likes to imagine “politically correct” commissars are out to martyr them. But expressing outlandish or dangerous views while holding a public position may create a conflict, forcing you to choose.

Look at the very different cases of Tim Farron MP, the former Liberal Democrat leader and Toby Young, still hanging on to a powerful position as head of the New Schools Network (NSN).

Farron regrets saying gay sex was not a sin. When under pressure to clarify his views, he told a BBC radio interviewer last April: “I don’t believe that gay sex is a sin”. Now he is no longer leader, he re-recants and tells Premier Christian Radio he had “foolishly and wrongly” giving an answer that was “frankly not right”. He felt “remaining faithful to Christ” was incompatible with leading his party – though he could hardly have stayed after that disastrous election result.

Some Christians like to feel persecuted, thrown to the lions of humanism as victims of an imaginary “Christianophobia”, despite the UK having an established church with 26 bishops in the Lords blocking the oft expressed “will of the people” on such things as the right to die.

Farron was in an impossible position as an extreme evangelical, “Bible-believing” Christian. Though I would guess he cherry-picks his sins. He no doubt abhors lying down with a man as with a woman, but what of all those other bronze-age injunctions – not to wear two kinds of fabric or plant two kinds of crops in one field, let alone the uncleanness of women with periods?

He has every right to think any weird stuff he wants, but on the whole most voters will be disinclined to think anyone believing such nonsense is fit for high office. Time was when no politician would dare not to be a Christian: times have changed because in this democracy the people’s views have changed. He apparently found seeking the popular vote required him to lie about eccentric beliefs. He was in the wrong job in the wrong party. How could a primitive illiberal expect to lead a party whose USP is liberalism?

As for Toby Young, whose Free Schools Network comes up for a new contract shortly, how can someone who toys with eugenics expect to hold a post in education, where all classes and races should be treated equally? The revelation by the London Student newspaper that only last May he attended a secretive eugenics conference – “the London conference on intelligence” at UCL – raises questions about his suitability. And that’s leaving aside the porn, malice and misogyny.

He wrote in a conservative Australian journal only two years ago, “My proposal is this: once this technology [genetically engineered intelligence] becomes available, why not offer it free of charge to parents on low incomes with below-average IQs?” to address “the problem of flat-lining inter-generational social mobility”.

Despite the non-emergence of an “intelligence gene” and the predominant importance of environment over heredity, the far right’s search for reasons why the poor are inferior has a long history. Steve Jones, renowned geneticist, puts it this way: he points out that wealth is considerably more heritable than genes. He says moving to affluence increases a working-class child’s IQ by 15 points. As for super-breeding, Darwin asked a racing dog breeder how he succeeded: “I breed many and I hang many,” was his reply. Not so easy with humans.

Young’s New Schools Network is an odd beast, a charity drawing £2m, 90% of its income, from the state, to advocate and help people set up new schools.

The closing date for the renewed contract to the NSN is 19 January – though it has always gone to the same outfit. Toby Young earns some £90,000 per year as its head. There is, in the tender, no mention of applicants being fit and proper – or non-eugenicists.

Polly Toynbee is a Guardian columnist