Solar batteries are safe when used and maintained properly. But they aren’t infallible: have them installed according to manufacturer guidelines, by a proper professional.
The main risk is fire. A process called “thermal runaway” can occur with batteries, which is a chain reaction that just keeps getting hotter. This can happen in response to damage: think short circuits.
Something you might not know is that they also need proper ventilation (lead-acid batteries, at least). They produce gas that needs to be vented away, either actively or passively.