It varies.

I often give the example of HP Lovecraft. I'm a big fan of his stories and the Cthulhu Mythos. But it remains that he was a huge racist. How do I reconcile the two?

First, an author's works are separate from the author themselves. Second, in Lovecraft's case, he was a product of his time and upbringing. And third, and importantly in his case: he's dead. He has no ability to change beyond his passing in the 1930s. People can and do change all the time. If Lovecraft were around today he might have become to most left-leaning person in the world, but he never had that chance. There were indications, late in life, that he might well have changed.

But, he didn't. It remains that he was a racist in life, that will never change, and because of it there will always be people uncomfortable with his work. That is understandable, and I won't try to convince anyone that they should ignore it.