This is not true, and definitely not normal, in my experience. The start/stop system in my F-Type (and in the F-Pace) was disconnected immediately after purchase, with no effect of any kind other than eliminating the annoying stopping and restarting of the engine. At a traffic light the car does NOT go into neutral, the parking brake is NOT activated, and acceleration happens with no hesitation, clunking, jerking, or other bad behaviour.
It is clearly not normal that stopping the car (not the engine) would automatically engage Neutral. If the start/stop system is truly disconnected, it is non-functional!

 

Such behaviour would presumably re-engage drive when you press the accelerator? Try revving the engine in N and see what happens.

 

I disabled the auto start/stop on my 2021 F Type the day I bought it. I live in the mountains and frequently come to a stop on fairly steep inclines or declining roads. There is one place when I come to a stop sign on an incline, look both ways for oncoming traffic at the highway crossing and then accelerate fairly hard onto the State highway. I have never noticed any kind of hesitation, in fact it just hooks up and goes like a bat out of hell.

 

Shouldn't that be a cat out of hell? Or are you channeling Monty Python's Holiday sketch?