When living with stoves old enough to have pilot lights, I and my family have always had them turned off by the repairman to eliminate the fire hazard. The pilot lights were controlled by a small valve under the stovetop, in the small-diameter lines feeding the pilots.
The risk from turning them off that I know of is that the valve may not shut off completely, leading to a small leak of unburned gas (since the pilot flames are no longer burning the gas constantly).
After the pilot lights are turned off, I recommend using a handheld piezoelectric or flint lighter to light burners; these can be found in camping stores. (They are easier to use, safer, and simpler than the more widely available butane lighters which have their own flames, because they directly ignite the gas with just a spark. However, they cannot be used to light candles or other non-gaseous-fuel fires, and in our experience are not effective in lighting ovens, for which we used matches instead.)