I just assumed that the second theory was right and they were mimicking Odo to make him feel like he'd really found his people. At first anyway. After that it became their default when dealing with people from the Alpha Quadrant because Odo had already established what they expected a Changeling to look like.
We at least know the hairstyle doesn't come naturally to them because Odo got that by mimicking his dad, Mora Pol.