I know the law of fasting is a law that applies to all the church members. But at the same time, it is not required for entering the temple or to have Church callings. How serious is not fasting in the Church? Could someone be called as Stake President or a Bishop without having fasted before?
Fasting is a practice that is deeply personal in nature because the reasons for the fast can be practically anything. We are encouraged to fast on the first sunday of every month, and for the most part this is considered sufficient for most any spiritual needs. Of course one may fast at any time for any reason, however it is not a requirement from the church.
Now, not fasting, as you have noted, has no direct impact on worthiness before the Lord as far as temple recommends go. Indeed there are even medical conditions that preclude the ability to fast in order to maintain good health. In the end, however it is all to be determined between yourself and Heavenly Father.
Fasting is intended as a regular practice to not only focus ourselves spiritually, but to maintain mastery of our bodies, that our appetites and passions always stay under our control. There is no interview that I am aware of that asks if one fasts or not. Not for any calling that I can imagine.
In answer to your question I suppose the answer would be yes, a bishop or a stake president can be called without having fasted. I have to say here though, that I’d be interested in knowing how often it has occured. It can’t have been too often.