~150 WS2812b LED's with Pi Zero and SN74AHCT125N
It most likely does not burn the LEDs, but it may not work properly either.

There is no bypass capacitor for the 125 chip. Put a 100nF ceramic capacitor directly at its power supply pins, so that there are no extra wires in between. If the waveform still has problems, perhaps a 22 to 33 ohm series resistor at the output helps if the wire to LED strip is long. The AHCT type is capable of high speed operation so it will have very fast transitions at output.

Also the unused gates of the 125 have their data and enable inputs unconnected, connect them to VCC or GND so that all chip inputs do not float.