Resistive touchscreen - when measuring X, why doesn't Y affect the reading?
Following on from your description...

When you read X, you connect X1 and X2 across a known voltage. A press will create a potential divider at the press position. The potential divider produces a voltage proportional to the X position of the press.

That X voltage is read through a Y resistor. There will be a voltage drop across that Y resistor of, from Ohm's Law, Vry = Iry x Ry.

There will be an ADC on the other end of Y resistor Ry, ready to convert the X potential divider voltage to a binary number.

So if the current taken by the ADC input is kept very tiny then the voltage drop across Ry will also be tiny. Then the voltage that reaches the ADC will be almost exactly the same as the voltage at the X potential divider.

The actual definition of what's too small an ADC input current to disturb your X and Y resistances will depend on the resistance values in your touchscreen. 

It's not difficult to make an ADC circuit with a very high input impedance, that draws practically no current from the voltage source that it's measuring. Either a suitable ADC can be used directly or the voltage can be passed through an op-amp buffer (with a gain of 1 ) with a huge input impedance.

You see a similar thing when you use your voltmeter to read the touchscreen as that has a very high input resistance.

The same principle is used for the Y measurement.