French rightwing groups who mobilised against same-sex marriage have threatened further social unrest to protest against the promotion of Najat Vallaud-Belkacem, an outspoken proponent of gender equality, to the post of education minister in the new government unveiled on Tuesday.

"I'm horrified," said Ludovine de la Rochère, the leader of the Manif Pour Tous, which staged mass demonstrations as the government struggled to push through the landmark legislation adopted in May 2013. She described the appointment of Vallaud-Belkacem, who was closely associated with the law, as a "provocation" and urged opponents of the minister to join a protest on 5 October.

Vallaud-Belkacem, who was minister for women's rights, youth and sport before becoming the first woman to take charge of the education portfolio, became a hate figure for the right when she backed an experimental reform introduced into 275 primary schools last year aimed at overcoming gender stereotyping. The minister was dubbed "Khmer Rose" by the rightwing Le Figaro, and was accused of importing the controversial gender theory from the US.

Vallaud-Belkacem, 36, told FranceInfo radio that "pointless polemics" would have no place in her ministry and that she was "committed to the equality of boys and girls more than anything else."

Meanwhile the left wing of the Socialist party was equally vocal about the government's fiercely pro-market course symbolised by the appointment of a former Rothschild's banker, Emmanuel Macron, as economy minister. Three leftwing rebels, including economy minister Arnaud Montebourg, were purged from the cabinet on Tuesday by the prime minister, Manuel Valls.

Macron, a former adviser to President François Hollande and architect of the government's business-friendly policies that have been promoted since the beginning of the year, is seen as the "anti-Montebourg" and was welcomed by business leaders.

But the Socialist deputy, Yann Galut, said he was shocked by the appointment of Macron, a 36 year-old political novice. Hollande had turned down a request from Valls to include Macron in his first cabinet five months ago on the grounds he was not elected. His appointment now "is an act of submission by France to Germany," said Galut. Macron said on Wednesday: "Judge me by my actions."

Gérard Grunberg, a political scientist with Sciences Po, told the Guardian that while the new "social liberal" government had clarified its line following the departure of the dissidents, "the war between Socialists and Socialists will now move to parliament."

Valls promised on Tuesday that a confidence vote would be held in September or October.

Grunberg said the lack of new faces in the government "showed how limited the political class is in France. It's narrow."