What can be safely attached to a gas furnace cabinet?

Best not to have anything close to a furnace. Our church got warned by the insurance inspector that nothing may touch the furnace and "stuff " should be a few inches away. Because they were in a large closet-like room people just stored stuff in it ,some touching the HVAC. These were two large capacity gas furnaces plus AC units as one would have in a large home.

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.