If you turn the hot water tap on at another faucet in the house then the hot water pressure that is going to the shower is reduced since the hot water would be flowing to the other part of the house to reach that faucet.
The change in hot water pressure can affect the showers temperature and cause it to lose hot water and go to cold.
You can have a shower mixing valve installed on the shower to prevent the shower from going to cold or hot since the shower mixing valve regulates the waters temperature by automatically adjusting and regulating the water pressure and temperature.