There are at least a couple of short stories about islands with maneating fungi. One is "The Voice in the Night" by William Hope Hodgson, an older writer who was appreciated by, and may have influenced, H. P. Lovecraft. This story is available at Project Gutenberg Australia and Librivox. Here is a review from E. F. Bleiler's Science Fiction: The Early Years:
Somewhere in the North Pacific, the narrator who is fogbound on a
small vessel, is hailed by an unseen man in a rowboat. The
circumstances are suspicious, particularly when the stranger, who asks
for food, will not come close to the ship and insists that the lights
be extinguished. But the compassionate sailors float a box of supplies
to him. Some time later the invisible rower returns and tells his
story from out of the fog. Victims of a shipwreck, he and his fiancee
have been living on a nearby island that is covered with fungi. The
fungus is not only omnipresent, but some examples are shaped like
trees and humans. The narrator and his fiancee tried to avoid the
fungus, but after a time observed that it was sprouting on them. There
was nothing they could do, for even carbolic acid would not kill it.
When their food was nearly gone, they yielded to temptation and began
to eat the fungus, though with strong feelings of guilt. They do not
expect to live long. As the stranger moves away, the fog lifts for a
moment, and the sailors see what seems to be a blob-shaped fungus in
There is a Wikipedia article about that story. On the ISFDB page you will find an extensive (but possibly incomplete) list of anthologies etc. where the story has appeared, and the contents of said anthologies; if you read "The Voice in the Night" in one of those books, you might recognize some of the other titles. Finally, the story itself may be on the web somewhere; I didn't look very hard for it.
I think Hodgson's "The Voice in the Night" is the most famous story on that theme. A later and less famous one is "Fungus Isle" by Philip M. Fisher; the reprint in Famous Fantastic Mysteries, October 1940 is available at the Internet Archive. Here is Bleiler's review of "Fungus Isle":
Longish short story. * The narrator and two friends are shipwrecked on a strange island south of New Guinea. The island is covered with fungi of the most extraordinary and extravagant sort; some specimens are even humanoid creatures that walk about. * It is soon learned that the fungi are a peril, for their spores will settle on human flesh, transforming a man into a walking mushroom. The only remedy for such infection is salt water, which kills the spores and plants. * Food and drink are problems. The fresh water is polluted and getting to it is most perilous. Succumbing to hunger and eating the fungus is fatal, for the fungus flesh conveys a mild sort of ecstasy and is immediately psychologically habit forming, leading to loss of personality and eventual insanity. Finally, the shipwrecked men—acting on hints from the humanoid fungi, who are transformed sailors—find a boat, which they clean off, and put out to sea. * Probably suggested by W. H. Hodgson's fungus stories "A Voice in the Night" and "The Derelict," but independent in development. Some highly felt moments of terror and horror, described in remarkable detail, but sometimes carelessly written.
UPDATE. In neither story are the horrid growths predominantly red in color; unless that detail is misremembered, both candidates must be rejected. Hodgson's fungi are characterized by a "loathsome greyness". Fisher's are a riot of colors:
The panorama before us was a horrid futuristic conception in ugly splotched colors—purples, yellows, browns, vermilions, and hideously mottled green grays. The mass of it repelled. The eye was tormented, the senses appalled. The colors were monstrous, loathsome—as though reeking with the deadly poison of an unclean and obscene living malignance.