The institute has published a booklet to gain support
The Christian Institute has said that teachers should not be forced to promote gay rights.
The comments come as the General Teaching Council for Wales is in the process of drawing up a professional code of conduct.
Part of the draft document insists teachers must respect the rights and needs of their pupils and colleagues in areas including family background, race, and religion.
Although the charity supports most of these guiding principles, it is opposed to the section of the code which refers to respecting pupils and colleagues' sexual orientation.
The charity has published its own leaflet, attempting to gather enough support to have the clause removed.
It has said the advice on sexuality marks a moral shift in education, forcing some teachers to be tolerant of gay rights.
The draft code is out for consultation until the 21 September.
The teaching council has said that because the code is still at the discussion stage, any comments are welcome.
This latest row comes the day after a conference in Cardiff heard how homophobic bullying was a major problem in schools.
More than 200 people attended the event which was aimed at tackling gay hate crime and judgmental attitudes towards young gays, lesbians and bisexuals.
Executive director of the gay rights group Stonewall, Angela Mason insisted that more needed to be done to stamp out prejudice.
Homophobic bullying
Ms Mason said: "There is a major problem of homophobic bullying in schools. We know this from what pupils say and what teachers say.
"Young kids experience worse assaults and more violence than adult lesbian and gays.
"We feel that it's because it's not being challenged in schools.
"It's not a matter of having one lesson. It's a matter of a whole school approach. They have to ensure it's a safe life for everyone at school."
Section 28 currently prohibits the promotion of homosexuality by local authorities in England and Wales.
Stonewall claim that this makes it difficult for schools to deal with the issue.