1.It means this thing is not contradictory to another one. 2.it means two dates are both ok.eg:I have an appointment today,and I'll attend a meeting tomorrow,so I am free both these two days.Then I can say:约会和会议这两件事是不冲突的.

It could mean two parts are not conflict each other, or they are not against to each other. Based on the context.

I think it means something is not contradictory.