What tolerance do typical components have to wrong-polarity voltages/currents?
It's hard to say what "typical components" are, but generally, a proper multimeter's continuity function isn't enough to harm most things. A good meter will apply a small voltage through a moderate impedance, so the total power that the meter could deliver to the device under test is very small. Even if the resulting current and voltage is outside of the component's specifications, there isn't enough energy delivered by the meter to harm anything.

My general advice: don't be afraid to poke around with your meter, unless you have specific reason to believe the device is sensitive or expensive. What you gain in knowledge and experience from experimentation is worth much more than the small chance of damage.