What type of shower are we talking?  Electrically heated?

If so, by their nature, they heat the water to different temps by adjusting the flow through the heater.  Opening a tap somewhere will reduce the flow and cause the shower temp to rise.

You can get thermostatically controlled electric showers these days, designed mainly for the infirm, they are costly but do away with the scalding issue.

If it is a mixer type shower, it is likely a thermostatic type anyway which will keep the temperature constant by adjusting the hot and cold accordingly.

Plain shower mixer not thermostatic?

Long pipe runs of wrong bore?

Scaled up pipes or valve not fully open?

High flow rate shower on otherwise adequate pipes?

Poor flow rate from the mains?

How to avoid...

Buy house in area with good mains pressure and flow rate.
Soft water area to avoid need for water softner (which looses some pressure).
Large bore, short pipe to the house.
Mains pressure stored hot water system.
Dedicated >22mm pipes from tank to the shower (Separate pipe runs for other outlets such as bath and taps).
All valves to be full bore types.
Thermostatic mixer shower.
Shower head with moderate flow rate. (Special care needed for high flow rate "rain" type heads and body jets).