It's not unusual to have fursuits participate in the DooDah Parades found in Pasadena, CA, and Ocean City, NJ, together with other places. They're not frowned on, actually, they're encouraged, due to the oddball nature of this particular parade.
However, some parades have their own set of rules. Check with the organizer before you take part in it. You may want to join another group if you're alone.