I’m wondering if it’s normal for the F-Type R to produce a loud thump from the rear under sudden, hard acceleration. It feels like an excessive amount of torque or power is being sent to the rear wheels.

The differential fluid has been replaced, the car drives fine in all modes, alignment is done, and it has fresh tires. There are no issues with daily driving or even hard acceleration while in motion.

The thump only occurs under sudden hard acceleration, typically from a stop or when accelerating quickly from a low speed.

Is this a known characteristic of the car?

 

It is really helpful in answering questions to know more information about the vehicle. I'd suggest adding vehicle information to your signature.

If it's an early model year there was an issue with the rear springs, and the remedy was to install buffers on the coils. If that's it, you're well past the point of getting it done under warranty. Other than that, I don't know of anything.

 

Just sounds like wheel hop to me?
Do you know how to launch the car? Do you race?
Many different ways you can vary it to minimize the rear wheel hop. It all depends on the surface traction and the amount and rate of power applied.

I have a 600+ HP XJR and it will hop under certain conditions too. A smooth and rolling action of the gas pedal will get you moving faster than mashing the gas pedal.

One BIG thing is wheel hop is very hard on the car and all it's parts. So when it happens PLEASE let off on the gas until the car recovers!
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yes your description sounds about right, it sounds like wheel hop.