Have to look that up when I have time. Never heard of red yeast. Maybe an old dog can learn something. :-)
It's not her saliva that's red...It's the bacteria in her mouth that turns the fur red.....Red Yeast then grows in the moisture......Karla
Not sure about the yeast but agree it may be the water.
Look at her food ingredients and see if there is any beet pulp in it, by chance.
It could be a couple of things. It could be red yeast. If her eyes tear a lot and the area around her eyes is often wet and if she licks her paws often, it could be that red yeast is growing in the usually-damp fur, staining it red.
Another possible cause is that her tears and saliva have a high concentration of minerals in them from drinking hard water. If you have hard water, you might want to try giving her bottled water for a while to see if the situation improves.
Ghilly