argue all you want, but it is not the job of HR to "fix" broken employees. It's the job of HR to remove said employees when they cause a problem, and make sure the company's ass is covered via documentation.
In my case during onboarding all of this is covered several times. "harassment or discrimination on sexual, racial, political etc grounds is not tolerated and is grounds for termination." There is no room for "I didn't know being a racist is wrong". If you somehow managed to avoid catching up to the rest of society over the past several decades then you're not someone who should be employed. I'll hire someone who isn't an idiot, other racists will learn to keep that shit to themselves, and make all of our lives easier.
HR's job is to protect the company's interests. It's in the company's interests to not have bigots on the payroll.
your error here is thinking that it's HR's job to "teach" diversity and inclusion. It isn't. It's there to enforce it. It's not my job to teach you not to be racist any more than it's my job to teach you not to be an alcoholic, or not to steal from us. My job is to make you aware of the policy (which in the case of blatant racism is redundant imho) and enforce it. edit: every employee in my facility has about 40+ hours of state mandated training to complete every year. None of it is designed to teach you to not be racist, or not sexually harass employees. The reason why is because this shit should be obvious to anyone that's learned to walk upright. if I have to spend five minutes "teaching" you that racism and sexism are wrong, then you don't belong here.
and the federal government did this by bringing the hammer down on those who weren't compliant. When the governor of alabama blocked black kids from going to school he didn't get a written warning or a stern talking to, he got the national guard on his doorstep to show the feds weren't fucking around.
someone with poor judgement, which is another reason not to keep her around.