Assuming the ignition source for the furnace is a spark, versus a hot surface, the source of noise is probably the igniter. First thing, verify the burner is bonded to the electrical ground. The igniter is part of the burner assembly if it is an oil burning furnace.
If the bonding to the furnace is good, the next thing to check is if the furnace and stereo are on the same branch circuit, the same phase, or the same multi wire branch circuit. If they are, try moving the furnace to a dedicated circuit, the other phase, or a dedicated circuit.
If these all check out, verify what audio source the noise is coming in. For example, if the noise is showing up only when the turntable is selected, the stylus leads probably need better shielding, if it shows up on the tuner, perhaps the antenna lead needs to be rerouted, if it shows up on ALL inputs, the amplifier inputs needs shielding or the noise is coming thru the power lines.
How close is the stereo amplifier to the furnace? Does the popping noise show up on any other radio or sound equipment? Does anything else create noise that is picked up by the stereo? Things that make electrical noise include light dimmers, motors in mixers, dishwashers, AC units, pumps for aquariums, hairdryers, clothes washers, clothes dryers, etc.
Switch suppressors work with switched inductive loads and relay coils. They are typically a small capacitor and a resistor in series. They absorb the inductive kick of the collapsing magnetic field of an inductive load.