Lidia Thorpe has been censured for her protest against King Charles when he visited Parliament House last month, and Ralph Babet for offensive comments made following Donald Trump's election, after Labor and the Coalition joined to pass motions condemning the pair.

The Gunnai, Gunditjmara and Djab-Wurrung senator confronted the king while he was delivering a speech to dignitaries at parliament in October, accusing the monarchy of genocide.

She later claimed not to have sworn loyalty to the king when she took her oath at the beginning of the term, prompting questions over whether she was eligible to remain in the Senate.

Senator Thorpe was censured for her "disrespectful and disruptive" protest, which the government and Coalition said disrespected democratic institutions.

The parties said in light of her conduct, the senator should lose any right to represent the Senate "as a member of any delegation" during the remainder of this term of parliament — meaning she may no longer represent parliament in a coming trip to the Pacific Islands.

Senator Thorpe and Senator Babet were not in the chamber when the motions were put against them due to flight delays.

Speaking outside the chamber following her censure, Senator Thorpe said Labor and the Coalition were trying to shut down a black voice.

"You've only given me more exposure ... and if the colonising king were to come back to Australia, I would do it again," she said.

"[The censure] is a diversion away from the real issues in this country."

The senator criticised the government's decision not to delay the censure motion, adding "they probably held up the plane, who knows".

A censure motion is a serious but symbolic gesture that allows politicians to voice their disagreement of a representative but it doesn't trigger any practical consequences.

Senator Babet, who was elected under the banner of Clive Palmer's United Australia Party, posted remarks condemned by parliament as "hate speech" on Elon Musk's platform X after the election of Donald Trump.

His posts aimed at people of colour, people with a disability and the LGBTQIA+ community prompted widespread condemnation from politicians across the aisle.

The incendiary right wing senator has previously posted offensive content on the platform, including graphic footage of a declared terror act in Sydney where a bishop was stabbed, as a protest against online censorship.

Senator Babet was censured for "his inflammatory use of hate speech, designed to drive division for his own political benefit".

The ABC has contacted the senator for comment.

The government and opposition affirmed that all Australians no matter their race, religion, gender, sex, or sexuality were valued and welcome.

Responding to the motion against Senator Thorpe, Greens senator Mehreen Faruqi got to her feet to defend her former colleague.

"The truth is the British Empire and the colonial forces have inflicted huge suffering ... on First Nations people. But you want to shut that down, you want to tell them to shut up," Senator Faruqi said.

Senator Birmingham said the Coalition did not oppose Senator Thorpe's right to protest, but the way that she did it.

As he made his comments, Senator Thorpe entered the chamber where she interrupted Senator Birmingham to protest that the motion was moved without her in the chamber.

Senator Birmingham added Senator Babet's comments were "repugnant" and had no place in civil society.

He said while censuring would feed attention-seeking behaviour, it was sometimes necessary to make clear of the parliament's disapproval.

Former Liberal senator Gerard Rennick said while he would support the censures, he decried them as "political point scoring".