Asbestos tape-covered ductwork that is coming from the furnace leading to each vent in the entire house. Is it a bad idea to leave it as is without disturbing, or would replacing all hvac system coming from the furnace be a better solution?
Asbestos is OK as long as it doesn't get airborne. No reason to disturb it unless you're going to be renovating that area (and even then you may be best off leaving it).
I agree with some of the information in the post @isherwood linked. In my state as long as it is double bagged any home owner can remove any and all the waste no limit on the amount that goes to the landfill. I would recommend a high end respirator cartridge type if the job takes multiple days you should use a fresh cartridge each day disposing the old one when finishing for the day. Also a tyvek suit, gloves and boots taped at wrists and ankles. Then a small garden sprayer with water to wet the material down before it is removed and bagged the water spray further reduces the dust. This is how the professionals do it I have worked with them on a large abatement project when retrofitting a mill I worked in. I would take the precautions listed above and not have anyone in the house while the work is being done until a wipe down of the surfaces are completed.