Richard Page says he was discriminated against because of his belief it is best for a child to be raised by a married father and mother.
Andrea Williams, Chief Executive of the Christian Legal Centre, which is supporting Mr Page, said: "We need to understand what is happening here.
"Christians are being excluded from public office because of what they believe. If this continues, Richard will not be the last Christian to be barred from serving his community."
An NHS panel ruled in August 2016 it was "not in the interests of the health service" for Mr Page to stay on, after his four year term as a non-executive director expired earlier last summer.
At a preliminary hearing on Thursday, an employment tribunal judge decided the case was "crying out to be heard", despite the NHS arguing that the case should be thrown out.
Andrea Williams added: "This is remarkable. Before Christmas Theresa May said that Christians should be free to express their faith in the workplace.
"Since then we have seen the suggestion that public office holders swear an oath to 'British values', and Dame Louise Casey has said that 'it is not OK for Catholic schools to be homophobic and anti gay marriage'."
The 69 year old was previously sacked from his position as a magistrate over his views on same-sex couples adopting children.