The head of Ofsted has backed the teaching of same-sex relationships in primary schools after parents mounted a series of protests at a Birmingham school over lessons about LGBT rights and gender identity.

England’s chief inspector of schools, Amanda Spielman, said it was right that children were taught about same-sex couples – regardless of religious background – and that not everyone fits “a conventional pattern”.

“It’s making sure they know just enough to know that some people prefer not to get married to someone of the opposite sex and that sometimes there are families that have two mummies or two daddies,” she said.

Spielman told the BBC: “It’s about making sure that children who do happen to realise that they themselves may not fit a conventional pattern, know that they are not bad, they are not ill.”

Her intervention came after Andrew Moffat, the assistant head teacher of Parkfield community school in Alum Rock, Birmingham, became the focus of complaints from parents objecting to teachings about LGBT rights and same-sex relationships.

Moffat has developed an education programme called No Outsiders aimed at helping children learn about equalities and tolerance of difference. He has been awarded an MBE for his work and was this week named as one of the finalists in the running for a prestigious global award which celebrates inspirational teachers.

His school, which serves a predominantly Muslim community, has received 80 formal complaints from parents and there have been a number of protests outside the school gates. Last week Ofsted visited the school which was rated outstanding in 2016 to investigate the dispute. The report will be published shortly.

Moffat is one of 10 teachers from around the world to make the final shortlist for the $1m Varkey Foundation Global Teacher Prize 2019. Last year’s winner was Andria Zafirakou, an arts and textiles teacher at Alperton community school in Brent, north-west London.

The education secretary, Damian Hinds, expressed his support for Moffat. He said: “Following last year’s UK win, I’m proud that another three talented teachers from schools in England made the 2019 top 50 finalists, and that Andrew Moffat has made the 2019 top 10 finalists; I wish him the best of luck for the final.”

Ofsted later confirmed the school was re-inspected after receiving a number of complaints. A spokesperson said: “We support the right of school leaders to determine the curriculum as they see fit and in the interests of their pupils – free from hostile outside influence.

“All schools have a responsibility to prepare children for life in modern Britain and that includes encouraging respect for those who are different, for instance LGBT people or those of different faiths.”

Spielman said the vast majority of faith schools were managing to do that. She said: “This is something where we’ve got to have sane, rational discussion, to say – are there places where it’s not working well enough, that we can find better ways? But it’s proper conversation that will change it, not protests.”

The Ofsted chief, Amanda Spielman, says: ‘All schools have a responsibility to prepare children for life in modern Britain’. Photograph: Alicia Canter/The Guardian

Ofsted’s chief inspector added: “The essence of democracy is that we don’t all get our way. We accept majority decision which means there will always be things that some of us don’t like, but that is the very essence of it – accepting that we can’t have 100% of what we want.”

The winner of the global teacher award – who will gain the soubriquet “the best teacher in the world” – will be announced in March at a ceremony in Dubai during the Global Education & Skills Forum. The other finalists teach in Georgia, Brazil, the Netherlands, India, the US, Argentina, Australia, Japan and Kenya.

Jimmy Rotheram, a Bradford school teacher, and Emma Russo, who teaches physics and science in London, were in the final 50 for the prize, chosen from more than 10,000 nominations from 179 countries.