Question
I have read that it is a fungus on the grass. My concern, is it harmfull to
humans or dogs? I walk my dogs in a nearby park and the grass has this red
"dust" and it gets all over my shoes and my dogs feet and legs.

Answer
Anthony:

This question is medical, not landscape based.  I suggest that you ask it to a doctor, to an allergy specialist or to a veterenarian.

Rust and Red Thread are similar in appearance, both fungi, both red to orange.  The main danger in carrying the spores may be an allergic reaction to fungi.

A search of CDC literature turned up an article on Stachybotrus, a fungus found on decaying wood which can effect respiratory systems in pets and humans, along with other allergic reactions.  There are 154 documents listed at CDC linked to fungi and outside activities.

None of the ones I reviewed mentioned Rust or Red Thread.  I did NOT read them all.  You may, if you wish,  at URL:

http://www.cdc.gov/search.do?queryText=lawn+fungi&action=search&searchButton.x=2...

Personally, I have only been attacked by one fungus, internally, in thirty-some years of working outdoors.  that came from a leaf prick of a Chinese holly.  But I must be fortunate in resistance to common allergens.

Best wishes.