Does not look like any algae I know. Algae is green, blue green [ cyanobacteria, actually], brown or sometimes red. Not white. Might be fungal. You could dip the plants, and put some baking soda in the dip water. I'd use a couple tablespoons to a quart of water. It often kills fungus. Maybe try a a cutting first, see what it does, before you yank it all out.
Nerite snails may help. I have seen them eat fungal growth on wood, so they might well eat this if you get one or two. Don't reproduce in fresh water, very nice snail to have, excellent clean up crew.