There is a certain thought out there, especially as I have noticed when reading on Vedic practices, that particular stones are by their virtue connected to a particular energy of a divine being, whether this be planetary or among higher deities. The wearing of these stones, minerals or substances in a sense endows the wearer with the grace of that deity, or in the case of the statue increases the flow of the divine presence between the deity and the icon (such as I have seen described on one website of a temple raising funds for a diamond crown for Lakshmi). This is the same idea in regards to wear the rudraska beads. That this can be in common with thoughts regarding Hellenic theurgy cannot be mistaken that a substance could endow a greater connection to a deity by its natural virtues and clarifications through its creation through the natural processes. As such it is a matter of intense devotion to adorn oneself in substance, particular stones which corresponds to the given deity of one’s focus of devotion. Sometimes this is as simple as color associations of beads which is commonly found in African Diaspora traditions in which certain colors are placed together to represent a particular orisha.
For myself I consider it a little bit of both. There are very particular substances which are sacred to a given deity. For Apollon amber is perhaps the most notable material substance (not a stone but a fossilized resin), although modern associations also give to him quartz (the last mineral that forms in magma), carnelian, and citrine among others….typically stones associated with protection and purification. But also being that white is sacred to him on a whole, that purest color which contains the spectrum of colors within it, the color of light, I consider any white stone, shell, bone or wood to be appropriate, especially among substances that come in a wide variety of color.
To wear these, in my view, is to surround oneself continuously with some fragmentary presence of the deity through theurgy. I have rudraska and amber that I wear, but I have plans for ropes of adornment that can be worn as necklaces and twines around the wrists. Likewise my statues of my lord Siv-Apollon are adorned with amber, rudraska, and white howlite. It is more than an outward sign to others who know what to look for, but more over connects you to the deity on different levels in your worship. While not necessary, they can be enriching and powerful companions in your spiritual journey to wear these tiny particle beings of the god.