There is no known red coloured aquatic moss in the trade as far as I know. All tho Sphagnum rubellum moss grows in wet conditions and can colour red, but it's a rather difficult moss to keep alive in a relative warm indoor environment. But there is a Rhodophyta Algae (BBA family) that roams the trade sold as Red Moss truly named
Caloglossa sp. beccarii. I'm not sure if you want this one, since it is an alga and once you have it it might be there for ever-growing at places you won't like it to grow.
But this picture bellow titled Red Moss in a river stream in France says something like it probably exists... Yet not found by an aquarist/scaper... Maybe a matter of time...
No idea about its ID and if its a Red Moss in random conditions or maybe not a moss at all .. Would be nice to find out... For now, I can't help any more than this.
And there seems to be a Microsorum Pteropus sp. Red, never seen it for real it exists but rarely in the trade. There is also an M. Pteropus sp. Orange I've had, maybe still have dunno actually. But this one only develops Orange leaf tip under high light and CO². It could be similar to the Red version.
Then we have
<Lagennandra meebóldii Red> that is an Araceae family same as the Anubias it should be able to grow epi[hytic. With this plant, I also have no idea if it is/stays Red in all conditions.
I know there is a Facebook page from a Polish shop named "The world of Aquatic moss" you might want to check it out. They often offer rather rare mosses for sale.