It comes after the Christian bakery Ashers refused to make a cake supporting gay marriage last year, prompting the Equality Commission to threaten it with legal action.
The change in the law, called the Conscience Clause, would give people legal grounds to refuse certain services, if it contradicts with deeply held religious beliefs.
However three of the other main parts in the Northern Ireland Assembly - Sinn Fein, the Alliance Party and the Social Democratic Labour Party - all say they oppose the Conscience Clause.
Sinn Fein gathered enough signatures on a political 'petition of concern', which means the bill must have cross-party support in order to pass. This means the bill would currently not be able to pass in the Northern Ireland Assembly.
Democratic Unionist Party MLA Paul Givan, who drew up the Conscience Clause, told the BBC: "It's about the message you're being asked to endorse, not the messenger who's asking for it.
"Say someone comes in and asks for a cake saying 'I support gay marriage' - that's a direct form of communication you're asking this Christian-owned company to produce and they don't want to be forced to do that.
"I don't think that's unreasonable, I think that's tolerant and if we live in a pluralist, liberal society we need to make space for difference."
A public consultation on a private member's bill forwarded by Mr Givan finishes this Friday.