One of the recommendations from a leaked controversial review into religious freedoms, led by former Liberal minister Philip Ruddock, is to strengthen the right for schools to reject gay staff and students.
Protection of religious beliefs already exists in almost every state and territory jurisdiction, except NSW and South Australia.
But Morrison has talked down the prospect of expanding those laws.
"What that report that Philip has put together...is it’s focused on what is necessary to ensure a positive right of freedom for religion into the future," Morrison told Sky News on Thursday night.
"I don’t think if someone’s at a school that they should be kicked out because they have a different sexuality."
Shorten said the existing laws are "out of date, if in fact they were ever in date".
"If Mr Morrison wants to back up his statement, I will work with him to make sure that no child is denied human dignity," Shorten told reporters on Friday.
"What would we say to the government is this, as any parent, there’s no case, there’s no rationale to discriminate against kids based on their sexuality."
Labor's education spokeswoman Tanya Plibersek said she found it "wrong" and "frankly abhorrent" for a school to turn away someone based on their sexuality.
"I think the vast majority of schools are grateful to their skilled teachers and aren’t sending the bedroom police around to their place on the weekend to see who they are living with," Plibersek told reporters.
Morrison is planning to release the full Ruddock report before the end of the year, which will come with the government's official response.
However, The Sydney Morning Herald on Friday published all 20 recommendations from the report, which was handed to the government in May.
The review was commissioned following last year's same-sex marriage plebiscite to appease conservatives who feared the change would restrict their religious freedoms.
The Law Council's Arthur Moses said no blanket exception to anti-discrimination laws currently exist to allow private schools to expel students on the basis of their sexual orientation or gender identity, and no such exemption should ever be introduced.
“We should treat our children compassionately, fairly and with care," Moses said.
"We should never have laws that would traumatise or stigmatise our children – no humane society does that."