Michaelia Cash says no child should be suspended or expelled under religious discrimination laws

The government expects its proposal for institutions such as schools to discriminate in hiring in favour of members of their own faith will pose a test for Labor, but the opposition is waiting to see the full legislation before declaring its hand.

Equality Australia is concerned that the bill will be passed before legal protections are in place to protect LGBTQ+ students, and will be lobbying government and Labor MPs to make further changes to the bill.

Allen and Trent Zimmerman have reserved the right to cross the floor, as has the Nationals MP George Christensen who believes the bill does not do enough to entrench religious freedom.

It is still unclear whether the government will introduce the bill in the House of Representatives or Senate, where it faces likely referral to a committee inquiry and has also met resistance.

The independent senator Jacqui Lambie has also questioned the need for the bill and senator Rex Patrick has suggested conservative and moderate demands pulling in opposite directions will probably scuttle it.

On Wednesday Rennick said the government had yet to address his concerns on vaccine mandates and he still intended to withhold his vote or vote against legislation including on national cabinet secrecy and the clean energy finance corporate rule changes.

With the hardest edges of the bill preventing employers sanctioning employees for religious speech and the ability for doctors to refuse patients removed, Labor faces a difficult decision on the remaining provisions.

The bill still provides that statements of belief do not infringe anti-discrimination laws, which could override protections in Tasmanian law against offending, insulting or humiliating people based on other attributes; allows faith-based institutions to positively discriminate; and bans professional bodies from regulating religious speech.