This isn't going to be easy but no one ever said that writing is easy. Writing a bigoted character needs to be done with special consideration for your marginalized readers. There's a line between what the character represents and what you, the writer, actually believe. Your readers need to believe there is a distinction. Here are some things to think about as you're planning and writing a bigot.
Why? You should be questioning yourself.
Why does this character need to be x-ist? Is that the only way this character can work in your story? Is there another way to show that the character is despicable without subjecting your reader to words or actions that may be offensive, harmful, and triggering?
Are you writing a bigot because "it's a turbulent time," and white supremacy is a trending topic? To use the real pain and fear marginalized people are going through right now and spin that for sales is cheap, its also transparent - just don't do it.
Don't confuse this with taking inspiration from, referencing, or feeling inspired to speak out against things you are seeing today.
What kind of bigot are you writing?
Bigot A: A slur spewing, confederate flag waving, Neo-Nazi skinhead
Bigot B: A curmudgeonly old-timer who lets out one too many micro-aggressions to be shrugged off as old-fashioned ignorance.
I strongly advise against A.
Put yourself in the shoes (or glasses) of someone fro a marginalized group reading a book with a character that hates them. What kind of emotions are you experiencing as you read the words and actions of that character? What about this book would make you keep turning the page? Is it worth it to continue when at every turn you could come face-to-face with an active, hateful person? Or would you say "the real world is hateful enough" and close it?
An important note on slurs: Use them sparingly. If you must (do you really?) only use it in dialogue.
Bigot B isn't foolproof (nothing is except abstinence) but can be less harmful to readers.
In order to take care of your reader if you have a bigoted character another character needs to be the antitheses, to be and think oppositely. But as in real life it isn't enough to be different. Your character has to act different AND call out bad behavior. It can be directly (right to their face) or semi-directly (it needs to be addressed but not directly to the bigot). It helps the reader know that they're safe and the bigot isn't just "getting away with it" or worse, is the hero!
Here are some examples from books the have bigots:
In Carey Mulligan's Mudbound the unlikable racist father/ father-in-law Pappy is a bigot A mixed with B. Why it works:
1. It's historical fiction (this isn't a free pass). Having a racist old white man in rural Mississippi in the 1940s makes sense and is in many ways unavoidable. She doesn't have a racist in her story just because. In fact, if a character like that didn't exist it could be seen as historically inaccurate.
2. Laura one of the main characters hates him, is afraid of him, and tries to keep her vulnerable children away from him. Through Laura, we see that his words and beliefs are wrong. Carey Mulligan gives us a character with no redeeming qualities.
The Harry Potter Series, Lucius and Draco Malfoy.
Definitely A type bigots. They subscribe to the classic: "I'm X (pure blood) and I hate Y (non pure bloods) type of people because I know I'm better than them because I'm X and they are Y."
They take it further by not only believing that but also acting on behalf of someone who wants to commit genocide against non pure bloods. Here's why it works:
Just about every other character in the book is fighting against them! From Harry, Hermione, and Ron to Dobby to the entire Order of the Phoenix. Their sole mission to make sure the Malfoys do not win. In the meantime there are small victories over the Malfoys. Harry sets the slave house elf Dobby free from the Malfoy family and Hermione punched Draco in the face for calling her the slur, "mudblood."
As you can see having bigot in your story isn't automatically a terrible idea, but it needs to be thought through in ways that are different from the way you plan other characters. If you're planning a story and need a sounding board please contact me on my services page.