Antonia Tully, national co-ordinator of the Safe at School campaign at the Society for the Protection of Unborn Children, accused the government of undermining the role of parents.
Speaking to Premier, she said: "It is parents who should be taking the lead in guiding and protecting their own children from pornography and other online content which is unsuitable."
Education Secretary Justine Greening confirmed all primary schools will have to hold age-appropriate classes on relationships, while secondary schools will have to teach about both sex and relationships.
In a statement, she said: "Schools will have flexibility over how they deliver these subjects, so they can develop an integrated approach that is sensitive to the needs of the local community; and, as now, faith schools will continue to be able to teach in accordance with the tenets of their faith."
The proposals have been welcomed by Christian relationships and sex education charity Acet UK
Speaking to Premier, Gareth Cheeseman from the organisation said: "We're quite hopeful that this is going to result in a better provision for young people.
"We know that the majority of teachers want relationships and sex education in school but they're under increasingly pressure - for a variety of reasons - which mean they struggle to make enough time for it."
The education secretary warned statutory guidance introduced in 2000 has become "increasingly outdated" and doesn't address the rise of things like cyber bullying and sexting.
Gareth Cheeseman from Acet added: "Realistically, we recognise some parents don't feel able - maybe they never received the good information themselves - they just won't talk to their children.
"Those children end up being very vulnerable."
Justine Greening said parents will still be able to withdraw their children from sex education, however, Antonia Tully from the Safe at School campaign said she had some doubts.
She said: "[For] all other subjects in the national curriculum...I can't take my child out of a history lesson, I can't take my child out of a geography lesson.
"I don't see how parents are going to be able to withdraw their children from these lessons.
Click here to listen to Premier's Marcus Jones speaking with Gareth Cheeseman:
Click here to listen to Premier's Alex Williams speaking with Antonia Tully: