Carbon dioxide and oxygen levels are independent of each other, so running carbon dioxide in our planted tanks does not necessarily deprive livestock of oxygen.
However, high CO2 levels can still asphyxiate livestock. Even though plants produce oxygen during light hours, most tanks spend more time in darkness than light, so oxygenation is still important even in planted tanks.
Good gaseous exchange is easily overlooked but is highly important in maintaining good O2 levels and to prevent excessive build-up of carbon dioxide.
Gaseous exchange occurs whenever there is contact time and circulation between the water surface and deeper water layers in the tank. It brings tank O2 & CO2 levels closer to atmospheric concentrations. In our tanks this means that it off-gases CO2 while increasing O2 levels. This seems counter-intuitive at first, but it makes tuning CO2 levels much easier. To read exactly why this is so, head to this section of advancedplantedtank.com.
To have good gaseous exchange, have a decent amount of surface agitation, a clean water surface and/or use sump/overflow systems. I personally use surface skimmers on all my tanks but any device that causes circulation of surface and deeper layers of water in the tank will work.
Some fishes such as discus are more sensitive to high CO2 levels, especially when they need to be kept in slightly warmer tanks. Gas solubility decreases with temperature, so being extra careful with gaseous exchange is necessary in discus planted tanks.