In Leviticus chapter nineteen, verse nineteen, some of the laws in the Old Testament apply only to Israel under the old covenant. However, other rules are to those under the new covenant. Regarding the former, some made to keep the Israelites from participating in the pagan practices of their surrounding cultures. For example, the prohibition regarding mixing two kinds of material may have been based on the fact that pagan priests attempt to practice sorcery by combining two different types of fabrics into their garments. The verse, as a whole, addresses the principle of purity without mixture.
The importance here in this verse involves the forbidden mixture of two different kinds: for example, cattle usually of themselves gender with a diverse specie, unless directed and solicited to it, as a male of one class with a female of another. For instance, a horse with a she-ass, he ass with a mare, and even creatures that were like one another, yet of different kinds, were not to mix. For example, a wolf and a dog, a hound and a fox, goats, and roebucks, goats and sheep, a horse and a mule, a mule and an ass, an ass and a wild ass; for though they are like one another, they are of different kinds.
The laws of the Old Testament regarding mixing somewhat apply today in the New Testament in terms of believers mixing with non-believers. The challenge for followers of Christ is to be a witness among those who do not serve and yet know God and simultaneously not fall into the temptation to follow the ways of society. The mixture of a believer and non-believer do not go together because light ad darkness will not work. One side will eventually contaminate the other. Either the light will prevail over the dark or vice versa. How much do we love God that we are willing not to get mixed up with the ways of the world?