A mattress should be viewed together with the bed base. A very soft combination of mattress and box-spring is not likely to cause back problems (only when sleeping in the prone position, which for various reasons is not recommended). On a mattress-bed base combination that on the other hand is too firm back pains could very well be developed or be aggravated. Both when sleeping on your side as well as on your back.
On a soft mattress the body sinks more into the mattress and the legs are relatively higher than the rest of the body. As a result the pelvis is less distorted, which causes less lateral tension in the lower back.
In general women have wider hips and tighter waists than men. Therefore women are better off with an even softer combination of mattress and bed base. If you need softer support -instead of buying a new bed base or a softer mattress- a good solution may be to use a soft memory foam topper, which you place on top of your mattress.