Polling RPNXYI at regular intervals to check for touches on the screen can be made to work, but it lacks reliability. Therefore, upon your advice in other such topics I connected the penirq now. This correctly detects clicks, but it also is pulled down when calling either of the RPNXYx-functions. So, when reading the data in response to the penirq interrupt, causes a new interrupt, and another one, etc.

How should I read the touchscreen click without causing an endless loop?

 Disable the "PenIRQ" interrupt before issueing "RPNXYx", then enable the interrupt after reading the data

Is there any code example available where it actually works?

It's depends on your circuit and your controller.

I use i2c.

It's not regarding I2C.

The PENIRQ only pull low when touched on the screen or processing "RPNXYx" commands, you can disable the PENIRQ interupt during your controller processing "RPNXYx" command, then enable it again, this is upon your circuit and your controller hardware. usually like this:

1) enable PENIRQ pull low interupt

2) in PENIRQ pull low interupt routing, disable PENIRQ interupt, send "RPNXYx" command, read out data, enable PENIRQ pull low interupt 

I know the general principle, but this is no code and so it can easily do away with things such as timing. Without a working demonstration I will remain convinced that it cannot be done.

If you know how to disable/enable interupt, then it will be easy, for me, only 2 lines of extra code:

GIE=0;

//send RPNXYx to display

//waiting and read data from display

GIE=1;

The GIE is global interupt control bit in all PIC controller.

For Arduino, use noInterrupts() and Interrupts(), different MCU use different code, you need to refer your MCU manual.

The interrupts pose no problem at all. But what is this:

//waiting and read data from display

I either get no response (device not ready) or a timeout.

Or, in case of RPNXYI, nonsense coordinates (&xffff or 40800 or something).

You even don't need PENIRQ, just use "RPNXYI", if the first byte of data is 0xFF, then means no touch on the screen. you can put this check in a timer interrupt.