Earlier civilizations, particularly in Asia, have attributed gemstones with magical properties and astrologers have assigned gems of certain colours to the twelve Zodiac signs. From this, and with the helpful support of jewelry makers, we have the Birth Stone Cross.
A birth stone attached to a cross is understandable to a certain extent. We like to personalize things and our vanity betrays us from an early age.
In elementary school we write our names on our pencil cases. Years later in adulthood we discover that demand for personalized car number plates pushes the price up to thousands of dollars. (Vanity often disappears in old age: Our name is written on a plastic wristband because we've forgotten who we are!)
Different birth stones for different members of the family can be used to make a Family Cross. (See also the Diamond Cross)
Use of such stones does not necessarily mean the owner wishes to make any astrological association. They are just a convenient way to personalize the cross. Such vanity, however, is undoubtedly a display of self-idolatry and pride; unfitting for a Christian cross.