What happens when both sides of a bi-directional MOSFET logic level shifter try to drive it and how to make sure terrible things don't happen?
Driving the single MOSFET level converter is done with driving circuits described as "open collector" or "open drain". This type of driver can only sink current. The only source of current in the translator circuit are the two pullup resistors.

So as long as either driver can sink the current sourced by both pullup resistors the is no concern regarding overload. And in this instance it is fully safe if both drivers want to turn on and sink current at the same time. No harm done. 

Be aware that this type of level converter is often used in an I2C interface. In these the SDA line is always bi-directional so there you have another confirmation that you can use the circuit in a bi-directional manner as long as all the drivers are current sinking only type drivers.