Would an electric furnace prevent outside air from coming inside my house?
You should investigate and upgrade the filtration of your air circulation rather than replacing your fuel burning furnace with an electric one. You need air exchange with the outside to get the oxygen you need to live.
Though one upgrade I would investigate in is a dedicated intake for your furnace, that way it gets fresh outside air (which after burning goes straight out the chimney) instead of using the basement's ambient air and pulling it into negative pressure which leads it to suck in air from all around the house.
In a properly functioning furnace the combustion air and the circulating air are kept separated. CO poisoning is way too dangerous to allow for any intentional mixing.
You can add a intake fan in your basement fed from the clean air at the other side of your neighbour to avoid sucking in their soot. You can also add additional filtration to this intake (make sure to regularly replace the filters). If this intake is enough for the basement to be at positive pressure it will prevent the basement from sucking in your neighbour's polluted air.
You could also add a lockout to the furnace to prevent it running while the pollution is too high in your basement.