There was a time in the United States when families actually felt comfortable going to work and to bed without locking their doors. People felt safe then, and there was little need to lock themselves inside at night. (My own parents, living in Florida, never locked their front or back doors for several decades prior to the 1980s.) In the case of the Curtis Brothers, they, too, must have felt safe in their neighborhood even though it was on the wrong side of the tracks. More importantly, they left their doors unlocked so that their friends--other greasers--could crash there if the need arised. With Johnny always fighting with his parents, it was a place for him to get away from the constant arguing. Two-Bit and Steve often visit the brothers in the early morning--Steve on his way to work with Sodapop at the gas station, and Two-Bit just to hang out. It was a symbol of the brotherly, family-like atmosphere that separated the greasers from the Socs.
Thy never Locke the door because they wanted people that they knew to always be welcome and be able to help anyone out. This shows that the Curtises are caring and want to help others out
If one of the members of the group needed help they would run in thru the front door.