I found that the balanced output of my BH-250 is too hot for my mixer board. I use post EQ settings and a passive bass. When I switch the input setting to "active" the signal is then OK. Is this normal?
It is not unusual. The "passive" and "active" gain range names are supposed to be a guideline and usually work in most of the cases. The way the ranges were defined is based on a large number of basses that were tested, before setting a value.
Your bass even if it is passive, probably delivers a signal that is higher than average for the "passive" range, and the result will be a saturation of the signal (but no clipping).
So the solution is just to switch to the active position. This should not affect the tone of your bass.