Kemi Badenoch has said “not all cultures are equally valid” when it comes to deciding who should be allowed into the UK, as she expressed her shock about “the number of recent immigrants to the UK who hate Israel”. The Tory leadership contender, who says she speaks with “conviction and clarity”, called for a new integration strategy that will take into account the fact that not all immigrants will “automatically abandon [their] ancestral ethnic hostilities at the border” as “their feet may be in the UK, but their heads and hearts are still back in their country of origin”. Writing for the Telegraph, Badenoch insisted the Conservative party “lost trust because we promised again and again to lower migration and failed to do so”. “Our country is not a dormitory for people to come here and make money. It is our home,” she wrote. “Those we chose to welcome, we expect to share our values and contribute to our society. British citizenship is more than having a British passport but also a commitment to the UK and its people.” Badenoch is running for the Tory leadership against Robert Jenrick, James Cleverly and Tom Tugendhat. All four Tory leadership candidates will get the chance to make 20-minute speeches at the conference on Wednesday, before the competition will be whittled down to two contenders. The final result will be declared on 2 November. She has attempted to set out a hard-nosed policy on immigration, insisting leaving the European convention on human rights will “not solve all our immigration issues”, and calling for a “wholesale strategy that starts with what kind of country we want to be”. Asked about her comments later on the BBC’s Sunday With Laura Kuenssberg, Badenoch suggested cultures where women have fewer rights than men were among those she deemed “less valid”. She said: “It is not about labelling cultures. Culture includes a lot of things. I am not talking about cuisine, I am talking about customs. “I think that cultures where women are told that they should not work; I would knock on doors … and you would see somebody at the door who says: ‘I can’t speak to you, I will get my husband.’ I don’t think that is as equally valid as our culture. “The point I was making in the op-ed was about immigration, that immigration is something which we need to make sure we get right.” She later added: “I am making an observation that we need to make sure we uphold our values in this country and we don’t allow it to turn into the place that millions of people around the world are running from.” She was also asked by Sky News’s Sunday Morning With Trevor Phillips if she was referring to Muslim immigrants when she wrote in the newspaper: “We cannot be naive and assume immigrants will automatically abandon ancestral ethnic hostilities at the border, or that all cultures are equally valid. They are not. I am struck, for example, by the number of recent immigrants to the UK who hate Israel. That sentiment has no place here. We must recognise that the world has changed.” Badenoch replied: “It is not all Muslim immigrants. And this is what I don’t do, I am very careful when I speak.” While rejecting the broad-brush accusation, she went further: “But there are some, those who buy into Islamist ideology, political Islam, they do not like Israel and we need to be able to distinguish between the two. That is why I don’t just use a word that brings so many people into the group.” When challenged about her blunt style of speaking, Badenoch indicated she would “swing back” when challenged to an argument, and rejected the idea that she was “too Nigerian” for British politics. In the same interview, Badenoch said she would be congratulating Benjamin Netanyahu if she were the Conservative party leader, after Israeli airstrikes killed the leader of the Lebanese militant group Hezbollah. “I think what they did was extraordinary. Israel is showing that it has moral clarity in dealing with its enemies and the enemies of the west as well. “Hezbollah is a terrorist organisation and I think that being able to remove the leader of Hezbollah as they did will create more peace in the Middle East.” The former foreign secretary James Cleverly urged Israel to act with “professionalism” and “restraint”. He agreed with his leadership rival Badenoch that Israel was “surrounded by people who would do them harm”, but insisted: “They have to act with professionalism and restraint.” Tugendhat said he would urge Iran to stand down its conflict with Israel if he were Tory leader.