If I have two logic gates (made of mosfets) with outputs connected to the same wire or bus, I encounter an issue where, when the logic gates are at opposite logic levels they are both trying to drive the wire to their respective voltage. This creates a current and a unreliable voltage across the wire. As you can see in the photo below, there are two OR gates connected to one another. I want the shared wire to be at logic 1 but it is being held at logic low because of the other gate. Also there is a large amount of current between the two gates. How to people deal with this?
If those gates are both "totem-pole" outputs (where they actively drive the output high or low) then that configuration is undefined and "illegal". For exactly the reason that you have discovered. The diagram you show is simply wrong and must be re-designed.
It is NEVER proper to connect the outputs from two active gates together.
There is a technique called "wired-or" where the node is passively pulled high with a resistor, and EITHER of the gates can pull the node low. But that requires "open collector" outputs where they can only pull the output low.
Simple answer. Do not hook them [push-pull outputs] together.
Ask yourself why you thought you had to hook them together. If it was because you wanted to signal when the output of either gate output was high level then the simple solution is to add a third gate to take the other two outputs and OR them into the final net signal.