Red Algae
The red algae (Rhodophytes, Rhodophyceae) are nearly all multicellular with a complex organization. There are no flagella at any stage in the life cycle.
that's a quote right out of your link. Seriously, if you can see that red macroalgae in front of you it is not a Protist. Don't want to get into a continuing arguement here, but IMO you are misinterpereting this just a bit. Algae are plants with a few exceptions. Protists is a kingdom added later after certain 1 celled or simple colonial 1 celled animals kept exhibiting both plantlike and animallike characteristics or even less than either other Kingdom's characteristics. It was a catch-all that took in a few representatives from many other animal/plant kingdom groups. But stuff like yeasts, bacteria and viruses is what the Protist Kingdom was really created for.
And after seeing many posts with a title "Algae or Plants" I have a feeling people may be getting a little off the path because algae are plants. So within keeping things simple and straightforward:
ALgae and vascular plants (and the several Phyla in between) are all PLANTS and you will keep out of most conflicts maintaining that distinction.
Please quote me the reference that says "MOST algae are protists", or are you forgetting the "pelagic one-celled or simple colony" part of the description? I just think you are causing some confusion just repeating portions of certain texts somewhat out of context IMO, but hey prove me wrong so we know the facts ultimately. Just in all my Bio classes(including microbiology) and all the texts and references I have accumulated, algae are mostly plants.
I know a whole gang of botanists that could eat all of us for lunch on this topic, maybe an email asking about the definitive current taxanomic heirarchy WRT algae and where can we get it will help.