It really isn't that big of a concern. The biggest difference in stress on the back is that the shoulders are hit slightly differently. The overhand grip spreads the weight of the bar across the whole shoulder, and the suppinated grip hits between the spine and shoulder blade. So yes, there is a slight imbalance. But a big part of it is just like your natural handedness. It's just going to feel more natural pulling with one hand suppinated than the other, just like it will feel more natural writing with one hand than the other.
For most people it's not that big of a deal. As you get stronger, you will have to use different variations of the main lifts to build more strength. It's not uncommon for people with 300kg+ deadlifts to pull with straps with the bar just below the knee as one of the variations.
If you are really concerned over the slight imbalance, or you develop some pain in the suppinated hand's shoulder, then I recommend the following:
- Add specific work for your shoulders, including external rotation exercise
- Pull double overhand on the warmups, and don't switch to mixed grip until it's really necessary.
- Pull heavier warmups off-handed, but keep the work set(s) with your strong side.
Personally, I employ the first two bullets routinely, but only occasionally do I switch my grip. Last competition my deadlift was 230 kg, and I'm stronger than that now. It wasn't until I got my deadlift over 200kg that I noticed any imbalances.