The Humanist Society Scotland group has long campaigned against current rules that mean Catholic schools are not obliged to teach sex education.
At the moment, Church schools will have a different curriculum when it comes to sex and relationships compared to other schools that can teach issues like pornography and sexting.
One in five young people in Scotland will be taught in a Catholic school, figures show.
The Society has launched its latest campaign after reports the UK Government was considering making sex education compulsory in all English schools. As education is devolved to Edinburgh this would not happen north of the border.
A previous campaign by the Humanist Society Scotland in 2014 failed to make MSPs support calls to force Catholic schools to teach sex education.
Chief Executive Gordon MacRae said: "Pupils in Scotland must not be left behind those elsewhere in the UK.
"We look forward to the Scottish Government reviewing their arrangements and removing the effective veto that faith schools have over the rights of young people to receive science based sex and relationship education."
A statement from the Scottish Government said: "Through the delivery of RSHP [relationships, sexual health and parenthood education], all children and young people are encouraged to understand the importance of consent, dignity and respect for themselves and the views of others."
The Catholic Church said its schools offer a "comprehensive programme of relationships and moral education...that promotes the unique dignity of each person, made in the image and likeness of God".
The statement added: "All relationships within Catholic schools are founded on principles of mutual respect and, like all schools in Scotland, there is zero tolerance of discrimination of any kind."