This isn't uncommon on the bike stand. If the headset bearings turn freely, the cables can easily exert enough force to "auto-center" the fork. Not a problem.

However, the cables shouldn't be stiff enough to affect the steering while riding. If they are, then you do have a problem.

Could you swap the cables inside the downtube? Some internal routings are open inside, but some have discreet internal tubing that would prevent this technique.
I.e., run the right/rear cable to the LEFT side of the headtube, and the left/front cable to the RIGHT side of the headtube, and cross them inside. So-called "crossover" cable routing makes a wider cable curve with a larger radius.