As long as your propane furnace is in good shape and there's no leaks in the lines leading from your propane tank to your furnace or any leaks at your propane tank then propane is just as safe as heating with natural gas.
Both propane and natural gas can explode if ignited by sparks or flames.
If you smell propane or natural gas don't do anything to create sparks, never turn a light switch on either or off because it can cause the home to blow up.