“We have a responsibility to ensure that all complaints are investigated without prejudice.”
The has been told the complaints were in relation to a post about Marieha Hussain.
Ms Hussain was found not guilty of a racially aggravated public order offence after holding a placard at a pro-Palestine protest depicting Conservative leader Rishi Sunak and former Home Secretary Suella Braverman as coconuts.
In one post on X, external, Baroness Warsi congratulated Ms Hussain on her acquittal.
Her resignation comes on the eve of the Conservative Party conference in Birmingham.
Baroness Warsi has previously criticised Tory leadership contenders Robert Jenrick and Kemi Badenoch.
She has also been a vocal critic of the party’s approach to allegations of Islamphobia and language used by Conservative politicians, including Ms Braverman.
She wrote on X: “It is with a heavy heart that I have today informed my whip and decided for now to no longer take the Conservative whip.
“This is a sad day for me. I am a Conservative and remain so but sadly the current party are far removed from the party I joined and served in cabinet.”
She added: “My decision is a reflection of how far right my party has moved and the hypocrisy and double standards in its treatment of different communities.”
Baroness Warsi suggested she would raise some of these issues in her new book, Muslims Don’t Matter.
In a further tweet, external, she said would “not be gagged on a point of principle” and accused the Conservative Party under Mr Sunak of wanting to “retry and replay” the trial of Ms Hussain.
“It would be unfair to do this whilst continuing to take the Conservatives whip,” she posted.
