Why does indicated stall speed change?
It happens because of a compressibility error in the airspeed indicator (yes, even in the digital ones, since the error is not mechanical, but a physical property of the air).

As you might be aware, the speed indicated on your instruments is not really a speed at all, it is actually a pressure. Your pitot measures a deltaP between static and pitot and displays that pressure difference on a scale noted in knots.. we call that Indicated Airspeed. 

This indication, because of changes of density, can be quite a bit different from your actual True Airspeed, but people didn’t care all that much about this difference, since the way the wing flies is reliant on that deltaP pressure difference anyway, so that you will actually stall at the same Indicated Airspeed, but not at same True Airspeed. (there is less density higher up but you are now traveling a bit faster, so the effect cancels out and the wing will behave the same)

The instrument was kept as it is in the cockpit (even though today we call it Calibrated Airspeed after a few changes) as a very usefull indication to the pilots.

Ok, now back to the question: turns out when planes begun flying faster and faster, a second error, caused by compressibility appears, that makes the airspeed indicator over-read. The pitot pressure is reported higher than it should be because at high speeds the air compresses in the pitot and makes the pressure there artificially higher, the deltaP is higher, thus our Indicated Airspeed is higher. Of course, this pitot tube phenomenon is not happening on the wing, so now we have a problem: we have a high speed indicated at the instrument, but most of it is actually just compressed air. Our Equivalent Airspeed is in fact much lower. And the wing will in fact always stall at the same Equivalent Airspeed. That means your Indicated Stall Speed in the cockpit will be ever higher as you climb because of compressibility.

Now, instruments were still kept to display IAS instead of the EAS, and a provision has been made where the stall barber pole advances up as you climb to make up for compressibility error

Then why haven’t the instruments been changed to show EAS directly? That is a harder question to answer definitively. I suppose by now people were already too used to having IAS in the cockpit, and the error is only really a factor for jet planes flying above (say) + 20 000 feet at speeds above Mach 0.5.