This type of reader has very good specifications regarding false-positives and false-negatives.
The basis of the technology is that it constructs an image of the fingerprint based on variations in the electrical resistance over the surface of the living finger - please note the word "living." The exterior surface of your skin, including the finger, is dead. Strip off the upper few layers of dead skin cells and you find the first layer of living skin cells. These skin cells have specific qualities of electrical resistance. They also composed into specific shapes over the surface of the skin. The combination of specific electrical qualities in the cells and specifically how the cells are arranged results in measurable and unique variations of electrical resistance over the surface of the finger. That is what a capacitive fingerprint sensor does - it reads variations in the electrical resistance of the living surface of the finger and constructs a map of the finger that shows those variations.
I don't think the variations caused by stress or illness would be enough to skew the reader to get a false-negative reading (user fails to login with correct finger). If you think about the fact that the user is dragging the finger across the reader at infinitely variable speeds (even though only a relatively small range of speeds will work), you'll realize that the mapping technology is pretty advanced, so the very slight variations introduced by stress or illness would not interfere.