Why specifically red algae with hard coral?
Hard coral sounds very general. Do you have some specific species in mind?
Dana Riddle ran a commercial coral farm back in the '90's. Multiple frag grow-out systems, literally thousands of SPS, 20 coral genera, perhaps a 100 species in this system.
He used (old) algae turf scrubber technology - quote - "The algae we grew were true turf algae and the pads were covered with various red, green, and brown types."
Now Dana to this day is still - "a proponent of algae scrubbers" or in other words, algae filtration. But he has a caveat - "if they use the right algae".
Dana reported that "red alga -(looked like the red alga Hypnea) would attack some of the corals (Acropora mostly) and bore into the skeletons. It made some sort of toxin that dissolved coral tissues."
OK, so this thread is focusing on suitable macro algaes to use in a refugium, specifically as a filtering method (Triton), as opposed to a macro algae display.
There are plenty of friendly green macro algaes that are suitable for the purpose of nutrient export that don't negatively affect coral. So I would be over cautious & refrain from using red algae to be safe as there is no need to risk it.