The OP understands that the distinction between ‘iron’ and ‘steel’ is pretty arbitrary, right? Wrought iron has less carbon than steel which has less carbon than cast iron, and the dividing point between what’s called ‘steel’ and what’s called ‘iron’ is based mostly on how iron was smelted in olden times, not on any clear distinct chemical difference.
(and then there are alloys like stainless steel, which is still mostly iron atoms…)
If you want a house that’s free of any kind of iron/steel, it’s going to be really tough. All the nails, screws, brackets, joist-hangers, and any other structural metal element are iron/steel. Some old post-and-beam houses might have wooden pegs holding the beams together, but good luck making anything recognizable as a modern wall without iron/steel (I suppose you could get some kind of custom-made exotic alloy nails for an outrageous price). And while electric wires themselves are copper, the outlet boxes, switches, etc are going to have steel/iron cases or moving parts. Hard to imagine any kind of electric powered appliance/lamp doesn’t have some iron/steel in the case (or the actual plug that goes into the socket). Just finding a raincoat without zippers, snaps, or metal eyelets is going to be an issue.