Can be minute warps in the record causing the cartridge to bounce and thus create the movement of the cones. Worth checking the downforce on your cartridge with a stylus gauge such as this - it could be running a bit light.
No, it's not dangerous. I would suggest that it is partly an amplification issue. I have heard absolutely thunderous low frequencies from a couple of LP based systems at higher volume levels with relatively little movement from the drive units due to very high quality amps being used. Either way, I wouldn't worry about it.