Is it important for a child with cystic fibrosis to be in a moderately clean and dust free environment?

Yes. Avoiding respiratory irritants is a good rule for a child with cf, but kids with this disease should not be restricted from living a life as normal as possible.
Yes. Moderately is the key word here. The germs that cause problems in children with CF often come from within them or from a hospital environment. Thus, while they should not be around other folks with cf, they don't need to be "kept in a bubble". Children with CF can also have asthma, so if allergies are a trigger, exposure to dust and other allergens can cause more symptoms. Playing outside is fine.

Related Questions

Does a child with cystic fibrosis have to live in a clean and dust free environment?

No. Clean helps & dust free helps for any kid. To some extent this ideal is relative and perfection on either point is unrealistic. With a stable hygienic environment, close monitoring by a CF center, & proper nutrition, these kids do well. Your CF center should have guidelines for healthy living they will share with you during your regular followups.