No need to throw your seedlings out just because of that. There are various organic and inorganic fungicides out there (check for one that specifically treats rust) that might lessen the problem. Think I have read about using some sort of homemade baking soda solution to treat it too, but can't remember it now naturally, lol!
You might try to keep from getting water on the foliage and do let the soil dry out just a tad between waterings. Fungus generally is more prevalent in moist conditions.

If you grow other hollyhocks in your garden you probably already know that this is pretty typical of the plant, rust and other foliar problems I mean. It is unsightly, but won't kill them (I've never had that happen anyway). Since it troubles my plants yearly (without fail by summer) I have just learned to ignore it or plant them in back of other things that will hide the lower half/foliage of the plants.
CMK

Thanks.... Last summer was my first successful hollyhock, LOL. I tried growing them the year before and the plants looked horrible; the entire plants were brown and diseased. I was thinking of moving some of the seedlings from this past summer's hollyhock to other areas, but I didn't want to spread disease around. I unfortunately never get around to spraying so anything I grow has to be healthy enough to look good on its own.

-lois, have you ever tried Alcea rugosa, the Russian hollyhock/fig leaf hollyhock? It is a yellow flowering species known to be a little more disease resistant that others. I grow it and it does seem to be FAR less rusty than my other old heirloom types.
I know what you mean. I usually don't bother to spray anything like that either, especially if it is just going to keep doing it or not clear up from spraying once or twice. I remember I tried that in my early gardening days, but gave up after going thru a bottle of spray and not getting rid of the rust, lol!
CMK

I have never tried it on hollyhocks because I never had rust problems with them, but I have used homemade rust spray on roses with excellent results. 1 TBSP apple cider vinigar to one windex sized bottle of water. Spray as needed. It might be worth a try.