If I'm registered as a charity with Stripe do I automatically get their charity rate?

No, you will need to apply for this.

Even if your Stripe account shows confirmation of your charity status, this does not automatically mean you are on Stripe’s charity rate.

To apply for the charity rate, you must email proof of your non-profit status to nonprofit@stripe.com.

Once Stripe has confirmed that your account has been approved for the charity rate, you can then update the rate in your settings. 

Click here for further information on how to do this.