I've lived most of my adult life in houses with forced air furnaces (albeit powered via natural gas, not propane), and what you are saying is inaccurate regarding indoor air pollution unless your furnace is in need of immediate replacement.
A modern furnace works via a heat exchanger, where the combustion produced pollutants never mix with the indoor air being pushed through. All pollutants are expelled outside via a property functioning chimney. This is one reason why you should have the furnace (and chimney function) inspected annually. Aging heat exchangers will show hotspots before there is a possibility of air being mixed, giving plenty of time to plan for a replacement. Of course there is a possibility of failure, which is why you should have a carbon monoxide detector.
A modern furnace works via a heat exchanger, where the combustion produced pollutants never mix with the indoor air being pushed through. All pollutants are expelled outside via a property functioning chimney. This is one reason why you should have the furnace (and chimney function) inspected annually. Aging heat exchangers will show hotspots before there is a possibility of air being mixed, giving plenty of time to plan for a replacement. Of course there is a possibility of failure, which is why you should have a carbon monoxide detector.