Parents who spent five months in mediation with teachers at a primary school in Birmingham over LGBT equality lessons have resumed protests after the school announced it would be relaunching equality teaching in September.

This comes as more than 50 MPs wrote to the education secretary, Damian Hinds, urging the government to show stronger support to schools on teaching about same-sex relationships.

Parents of pupils at Parkfield community school in Saltley staged weekly protests over the relationship lessons, which they claimed promoted gay and transgender lifestyles. In March, hundreds of mainly Muslim children, aged between four and 11, were withdrawn from the school for the day.

Just before Easter, the school announced the “No outsiders” lessons, which teach tolerance of diverse groups including those of different races, genders and sexual orientations, would not take place until a resolution had been reached.

On Wednesday, the school announced that a modified version of the scheme, “No outsiders for a faith community”, would be introduced in September. However, some parents immediately said they were not happy with the outcome of the consultation and protests resumed outside the school.

In a video clip seen by the Guardian, Mariam Ahmed, one of the parents, clashed with a member of staff at the school gates. Ahmed, alongside Fatima Shah, another parent, was the first to raise the issue with staff at the beginning of the year, saying children were too young to be learning about same-sex marriages and LGBT issues in class.

During the heated exchange, Ahmed is repeatedly told she is banned from the school. As Ahmed tries to gain entry with her daughter, a pupil at the school, and another child in a pushchair, the member of staff says: “You are not allowed on the premises. I will stand here until you move.”

The person filming the clip urges Ahmed to go around the member of staff before Ahmed becomes increasingly agitated and begins to raise her voice as her own children and other parents and pupils look on.

Ahmed says: “You are going to move from the front of my pushchair right now. Move away from my pushchair. My baby is here move now! Move … I swear to god get away from my pushchair …. Now you are aggravating me, my baby is here and my young child is here. Now move… We are not criminals.”

Ahmed can be seen shouting that her children are becoming upset before another parent intervenes saying the child is “getting scared” and takes her daughter into the school.

The school would not comment on the video clip but confirmed protests had resumed.

A spokesperson said: “This morning protests restarted outside Parkfield community school, which we presume are in response to the schools announcement that the new education programme – No Outsiders in a faith community. Following five months of consultation with parents, community representatives and the Department for Education, Parkfield community school will be relaunching this equality teaching in September 2019.”

Some parents said they voted against the modified programme. In a statement headlined “Parkfield parents show of solidarity”, it was revealed that some parents were banned from the school premises after speaking out against the new proposed programme in the year group consultations.

The programme was developed by the assistant headteacher Andrew Moffat, who was awarded an MBE for his work in equality education. It is taught by schools across the country, the ethos being to promote LGBT equality and challenge homophobia in primary schools.

The school was cleared of wrongdoing after an inspection by Ofsted, which ruled in its favour, praised Parkfield’s record on promoting “tolerance, acceptance and mutual respect” and confirmed its rating of “outstanding”.

Hinds, who has previously spoken in support of the school’s teachers, has been urged to provide further support for schools offering equality lessons.

A letter written by the Labour MPs Emma Hardy and Jack Dromey, and co-signed by more than 50 MPs and some members of the House of Lords, said: “We ask you to provide absolute clarity in regard to relationships education in primary schools, which must be inclusive of all protected characteristics, and treat the different types of relationships in our society equally.”

Referring to the recent demonstrations against equality teaching at Anderton Park primary school, also in Birmingham, the MPs say it is “unacceptable” that a school had a high court injunction against demonstrations outside its gates.

In response, Hinds said: “Our new guidance is clear that children should leave school having learnt about LGBT relationships, and I strongly encourage primary schools to teach about different types of family, including families with same-sex parents.”