Capacitor acting as a resistor
You probably won't be able to measure the change in capacitance between the strips being pressed together and not being pressed together, as it will be small, but it's still there. (I would guess that their self and mutual capacitance to be in the range of 0.1-10pF.)

A capacitor changes voltage by gaining or losing charge. They lose charge constantly to things nearby with a lower voltage such as the fabric, a grounded strip, or your finger if you are near ground voltage. They gain charge the same way, including from your finger if you have excess charge (higher voltage than the capacitor). If they aren't well connected to anything, they won't gain or lose charge/voltage quickly.

All components have capacitance, inductance, and resistance. Each of these is can be further broken down to self, the electrical relationship it has with its environment, and mutual, that with other components you are interested in. Resistance is always defined between two points or components, a mutual relationship, but you can imagine a self-resistance if one regards the environment as total passive electrical dissipation to ground.

In this case you are interested in the self-capacitance of the strips, the mutual capacitance between the strips, the mutual capacitance between each strip and whatever pressed down on them (your finger?), the resistance between the strips, and the resistance between each strip and whatever presses down on them. Pressing down on one strip, decreasing the space between them, increases the mutual capacitance between the strips, increases the mutual capacitance between each strip and your finger, decreases the resistance between the strips, and decreases the resistance between each strip and your finger. The increases in capacitance has the effect of allowing each strip to hold more charge, but it does not change charge/voltage in the strip by itself. The decreases in resistance has the effect of equalizing charge/voltage between the strips and between each strip and your finger, which, assuming one of the strips and your body is near ground voltage, lowers the strip voltages.

It sounds like you are trying to make a button or sensor. This is not typically done by sensing or using changes in capacitance between these strips, but by sensing or using the change in resistance, with extra capacitance (a capacitor) connected to one of the strips. For a normally-on button, one strip could be connected to low current supply (voltage supply with high resistance) and a 1-100nF capacitor, the other grounded; an interface that changes its resistance in response to your finger, pressure, or both, in between; and a low voltage amplifier such as a transistor connected to the charged strip, its output driving whatever you wish the circuit to accomplish (micro-controller input, provide power to LED, drive an audio amplifier, etc.). For a normally-off button, the variable resistance interface goes between the charging strip and the power source, and a large pull-down resistor is used in parallel with the strip capacitor.

It's hard to sense small capacitance changes in circuits that include widely variable components such as fabric, strip spacing variations, body voltage, body skin resistance, and body path to ground resistance. It's easier in well-controlled environments, like embedded under a Gorilla-glass layer in a cell phone. You could experiment with a function/signal generator and an oscilloscope to see how these variables affect signal throughput, as it can be done. I imagine a micro-controller detecting short-term (windowed) changes in the amplitude (envelope) of a ~MHz signal compared between the generator (strip A) and receiver (strip B). There are fancy radio circuits that I cannot begin to understand that may do the trick.