Logic Level Converter (3.3v  5.0v) returning HIGH for Low Volt. & High Volt. sides when nothing is plugged in. [Raspberry Pi]
Add a pulldown resistor (a 1k or so resistor to ground) to each input of the level shifter that you need to protect from erroneous activation. As a result, when the Pi is not driving the line, it defaults to logic low, and the level shifter outputs will only be high when the Pi is actively driving the corresponding inputs high. When high, about 3.3mA will be drawn from GPIO pins to overcome the pulldown, which is within recommended limits.

Note: The level shifter includes its own pullups (which cause the output to default to high), with value 10k. When the signal is low, both pullups on each channel need to be overcome (the LV pullup directly, and the HV pullup because the FET will conduct).
Your pulldown resistor should have a value that is small enough to be able to overcome these pullups.