The controversial bill has been dogged by claims that it would allow religious schools and other institutions to discriminate against people based on their gender identity and sexuality.

Border Catholic education diocese confirmed this week it would not expel trans students, even if the bill had passed without protection for gender diverse people.

A lower house debate on the bill went into the early hours of Thursday morning. Five Liberals crossed the floor to vote with Labor and independents to amend the bill - this time abolishing the right for religious schools to discriminate against gay and transgender students.

The bill passed and was due to be voted on in the Senate yesterday but the government retreated after NSW Liberal Andrew Bragg intimated he was prepared to vote against his party.

Catholic Education Sandhurst executive director Paul Desmond said the pre-amendment bill appeared to infringe on children's rights to equality in education.

"I am reading that this bill does discriminate against (trans children), which concerns me, anything that violates human rights concerns me," he said.

"I would be very concerned about any individual being denied their rights, and if that's in this bill then I'm not a supporter of this bill."

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Mr Desmond said that even if the bill were to pass without protections for trans students, Catholic Education Sandhurst would ensure the protection of all students.

"We're educators, we want only what's best for the kids, I don't think the churches would be supporting any legislation that would deny a child their rights," he said.

Catholic Education Diocese of Wagga Bishop Mark Edwards said they had no interest in expelling gay or trans students or teachers.

He is unsure of how a transitioning student would fit in at a single-sex school but said these matters would need to be worked out within school communities.

"I get that if you suffer gender dysphoria or are the parents or brother or sister of someone who does, a change like this would be an anxious time," he said.

"Certainly I'd say this isn't something we want to use against any students.

"I recognise there will be problems and challenges but we value that parents trust us to help form their students and we value opportunity to introduce children to Jesus. We're not interested in getting rid of staff or students."

Overall, Bishop Edwards supports the introduction of a religious discrimination bill to protect freedoms.

He said for him, the bill was important as it ensured religious people, whether Muslim women in hijabs or Catholic priests in collars, could not be denied entry or service in shops and other public places.

The other important factor in the bill he supports is the right of association.

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