What can be safely attached to a gas furnace cabinet?
The external surfaces of the furnace and ductwork are not hot enough to be a fire hazard with the items you listed. As we don’t know if this is a newer sealed combustion system or older gas vented system you would need to stay away from a vent they can be hot.
I would not hang heavy items like gallons of anything even if magnets could hold them the duct’s are not designed for this but light loads I don’t see a problem.
I probably would not put even 409 or any chemicals there I had one customer that used the main trunk line to the registers as a shelf. The heat cool cycles caused spray bottles to dribble when the heat was running the air in the bottles expanded dribbled on the duct and one of the bottles had a cleaner  that dissolved the galvanized coating and it started rusting. (My guess it was a slightly acidic cleaner as even vinegar will dissolve galvanized coatings).
I was able to clean the rust and use cold galvanizing spray to stop the rust she then put the stuff on a raised tray and that stopped the dribbling.
You don’t want stuff dribbling down the side.
I don’t see a problem with dryer balls anti static sheets or hanging a broom by magnets and would not expect any problems because of the magnets.