What do you mean by they do not compete? Of course it will affect one another. Its not a competition but rather volume of stable dissolved gas that water can sustain in given environment (simple analogy, warmer water has less dissolved O2 than cooler water).CO2 and O2 do not compete. Plenty of people diffuse CO2 through a filter. I have done it through a canister myself.
Try testing for [O2] in the tank after CO2 are diffused into water with no other factors changed and compare to tank with no CO2 injection.
[CO2] and [O2] are affected by each others and other dissolved gases and other factors etc, etc..
I was more concerned with availability of O2 for aerobic BB in an environment with higher saturation of dissolved CO2. Why take a chance by injecting CO2 into such when it can be avoided.
There are instances where this way of injection may cause enough disturbanceswhere other factors can contribute to disaters over night or when you are not home, especially with DIY system where injection is not properly controlled/monitored....
Lot less or no implications/complication yielded when CO2 are injected on return tubing right above the filter..