Operators can breach a soft wall using explosive gadgets and certain weapons. Some gadgets exist mainly to take the opponent by surprise by blowing up a wall and creating a breach. Shotgun shells can create holes in soft walls, but holes created by other firearms will not let you pass through as they don’t destroy studs.
As a defender, you can reinforce soft walls to make them more difficult to breach. However, some Attack Operators like Thermite and Hibana have gadgets to create holes in reinforcements to shoot or move through. These are called hard-breach gadgets.