Senior Liberals are disowning the party's hard-right vice-president Teena McQueen following her train wreck performance on the ABC's Q&A program.

It can also be revealed that the Liberal Party's most senior officials, including president Nick Greiner, had twice requested that she cease going on Sky's right-wing, after-dark programs. But she refused, saying the money she received to appear in her capacity as a party official was too much to relinquish, according to sources familiar with the conversation.

On Monday, Ms McQueen doubled down on boosting her media profile by appearing on Q&A.

During a debate about the line between free speech and hate speech in the wake of the Christchurch attack, and Senator Fraser Anning's comments attributing blame to Muslim victims, Ms McQueen said the "worst hate speech" she'd heard "recently" had been from Greens leader Richard Di Natale.