The Nazarite Vow gave the common man the holiness of the priesthood without the tidiness involved. We have Christ's holiness without a razor.
Grace gives us full identification without the constant need to groom ourselves. As a matter of fact we shouldn't groom ourselves in the matters of righteousness. Just as the Nazarite was forbidden to cut their hair.
The Nazarite had the same restrictions as the High Priest while he ministering in the temple without the responsibilities of performing the sacrifices or the lineage. Both were holy in the same degree. A holy person is just as holy as any other holy person in the old testament as well as the new. The priests however needed to have things in order. The hair needed to be neat and kept up even under their mitre.
The Nazarites identified with the priests' restrictions under the law.
We identify with Christ under grace. Not an Earthly priest but a Heavenly one... seated above separated from food, drink and death. He was in order and put the sacrifice in order so that we don't have to. We are holy as He is holy by identification and not grooming.