Believe me, THAT was a big concern for me too.
The reason I wound up using them though is ...
I germinate my seeds through the Winter. I have all the cups in the small plastic shoe boxes on a window sill so that once they start germinating, the warm sunlight will help them grow. At night in the window, it gets rather cold. The styrofoam seems to help insulate the plants and holds some of the warmth from the day through part of the night. That way the young seedlings don't get so cold that they stop growing or worse possibly die. Daylilies are hardy though, so that might not be a valid concern.
Also ... I have used paper cups and they deteriorate rather quickly. And have used plastic cups that I have found are often difficult for me to get the seedlings out of the cup without completely disturbing the roots. The styrofoam cups are much more flexible and easier for me, personally, to remove the dirt with roots in tact when I am ready to plant them out in the garden.
I experimented with different containers and the styrofoam won out for all these reasons. And I am NOT one who wants to further pollute the earth. That is why I mentioned in another comment NOT to use the deteriorating shredded cups in pots with edible plants! I do think they are toxic.
I will say that I get 3 growing seasons of use out of each styrofoam cups. I make them last for the reason that they are likely bad for the environment.
If anyone comes up with a better alternative to use, I would love to know about it!!!