Propane heaters are generally considered a safe and efficient way to heat. They do come with explanations of certain restrictions, dimension requirements and ventilation needs. In order to determine if they are safe for your home, you need to follow the instructions by the manufacturer and educate yourself with the information provided before you use one.
Both propane heaters and electric heaters attain their heat from a source. For a propane heater that source is a flame produced by a spark from the quartz crystal. The size of the flame is determined by a thermostat setting as is that of an electric heater. For an electric heater, the ability to heat is produced by the electrical outlet it is plugged into.
Some would consider an electrical outlet far more safe than a flame, but that is not necessarily so, although the electric company would have you believe it. The manufacturers of indoor propane heater produce both effective and efficient propane heaters.
The problem generally is caused by the user. Either a lack of understanding, or disregarding the instructions that come with the propane heater, can result in the homeowner finding himself and his family in a very dangerous situation.
Indoor propane heaters are made to provide a non-electric source of heat for small spaces and enclosures. It is necessary for these enclosures to provide enough space and air for the propane heater to work with the air in the room to avoid over-heating.
There have been accidents, which resulted in giving propane heaters a bad reputation, caused by people who put propane heaters in unsafe, small rooms without proper ventilation for the propane heater to work efficiently. That resulted in over-heating and the propane heater catching fire or exploding. Give those circumstances, they are unsafe.
But, by following the instructions and determining whether the use for which you are considering the purchase of a propane heater is sufficient to allow it to work in the manner for which it was manufactured.
Yes they are safe. They are also relatively inexpensive to buy and even more inexpensive to maintain. Periodic cleaning and correctly filling the tank when has emptied is much less expensive than the cost of electricity. There is no question about that.