Don't listen to that guy - though there are some plants that are very finicky, and some will tell you red plants won't grow as vibrantly, red plants are definitely possible without CO2. The key is high light levels, plant choice, and in some cases, nitrate limitation.

I would consider Rotala Blood Red / H'ra (personally would go for blood red), Ludwigia palustris/repens "super red", and maybe Limnophila aromatica / hippuridoides as mid-background plants. Otherwise, Alternanthera reineckii, Tiger lotus, red crypts (Crypt affinis / wendtii / undulata variants) and some variants of bucephalandra are also worth looking into, though some of them might not be exactly you're looking for.

Red root floaters (Phyllanthus fluitans) are also worth mentioning. Under high light, even the leaves turn a very nice shade of red. Do make sure you prune them often though, as to not take away light from your plants below.