1) Lithium batteries do not contain very much lithium.
2) Lithium in batteries is not in an pure, unbonded form. It is always in a bonded compound. Pure elemental sodium will react even more violently with water, but we put sodium salt on our food all the time, and nobody is afraid of moisture in their salt shakers causing explosions.
Keep in mind that people take (eat) lithium pills. It is only reactive with water like that in its elemental form.
Other common items that are massively dangerous in their pure elemental form, yet we consume every day:
a) Florine (floride toothpaste)
b) Hydrogen -- think Hindenburg explosion (water)
c) Oxygen -- in the form of O3 is ozone, which destroys lung tissue (water)
Any method of storing energy is potentially dangerous when that energy is released in an uncontrolled way. That's just basic physics. But being afraid of lithium batteries due to elemental lithium's reactivity with water, is like being afraid of your salt shaker due to elemental sodium's reactivity with water.
Or like being afraid of Gummy Bears: