Consider rules where forward and backward sequences give the same results, but where initial conditions are filtered by running the rule for a couple of steps.
Select[Table[RandomSMW[2,8],{10000}],InterestingRuleQ];
Select[%,With[{i=SMWStep[#,"ABAAB"]},(SMWTestEvolveList[#,i,20]==SMWTestEvolveListBackward[#,i,20])]&]
{{AABABB,BABBAAAA}}
MapIndexed[Show[LabelWrapper[GraphicsRow[{SMWXGraphicsStreamed[ChopEvolution@SMWEvolveListX[#,"ABAAB",20],2.5],SMWXGraphicsStreamed[ChopEvolution@SMWEvolveListX[#,"ABAAB",20,Backward],2.5]}],First[#2]]]&,%];
Select[Table[RandomSMW[2,8],{100000}],InterestingRuleQ];
Select[%,With[{i=SMWStep[#,"ABAAB"]},(SMWTestEvolveList[#,i,20]==SMWTestEvolveListBackward[#,i,20])]&]
{{ABABAAB,ABBBAAA},{ABBA,BBABAB},{BBAA,AABBABABB}}
MapIndexed[Show[LabelWrapper[GraphicsRow[{SMWXGraphicsStreamed[ChopEvolution@SMWEvolveListX[#,"ABAAB",20],2.5],SMWXGraphicsStreamed[ChopEvolution@SMWEvolveListX[#,"ABAAB",20,Backward],2.5]}],First[#2]]]&,%];
Show[SMWSimpleGraphics[SMWEvolveList[{"ABA""BAAB","ABBB""AAA"},"ABAAB",200]]];
Length[%152]
57