How can I get my parents to use the correct pronouns?

I would try having them read this article:

http://letsqueerthingsup.com/2014/09/15/what-youre...

Change isn't going to happen overnight, so have patience. A strategy that might work as a compromise for them is avoiding pronouns and using your name. That might serve as a bridge to using your preferred pronouns.

You don't say how old you are, but if you're 18 or older and things don't get any better I would suggest moving. Your psychological health will be better for it and it might actually help your parents as well.

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The correct pronouns are those that correspond to the person’s biological sex. “Genderfluid” is just a ridiculous, tiresome fad.

If you were born with a dick, they should call you he. If you were born with a pussy, they should call you she. If you somehow was born with both or neither, you habe a severe medical problem.

My tip for you would be to give them a break and don't try to make them change the habits of a lifetime for your convenience.

you might not be able to

Give them a time out. I’m serious. Tell them you won’t talk to them for a day if they mess up. Then stick to your guns.

They don't care because it's all kinda silly. :)

In English, "they," or "them" are plurals used for a group of people, and never a single one.  If you wish to redefine words in the English language, you have to expect people to have a bit of trouble with this.  Think of it their way:  why should they change their language just because you want to?  What if you want white to mean black, and up to mean down?

Learn to live with it. You can't change other people's behavior.

Your parents are not going to give in to that nonsense.  Grow up.