Bridging an amplifier effectively doubles its output impedance, which halves the damping factor. A 4 ohm speaker remains 4 ohms, but the amp's ability to stably drive the load is compromised significantly. So, you can safely bridge into 4 ohm speakers if the manufacturer has designed the amp to be able to handle 2 ohm speakers when used normally.
There's no correlation between a speakers output impedance & its sensitivity. However, most SS amps produce a lot more watts into 4 ohms than 8, so bridging tends to be more attractive to people with 8 ohm or higher speakers. The amps are more stable bridged into these loads. One thing to note, though - reducing the damping lowers the amp's control of the speaker. This could result in looser sounding bass.