What should I do about my sister’s refusal to celebrate birthdays and holidays?

Although we cannot presume to know your sister’s interior prayer life, you might point out to her that the Lord celebrated holidays during his earthly life (cf. Luke 2:41-43; John 6:3-5, 7:1-10, 10:22-23). In fact, one of the motifs of the Gospel of John is the Jewish holiday cycle. The purpose of holidays is not to worship days and individuals. It is to set apart time to focus attention on loving God and loving neighbors, the two great commandments (cf. Matt. 22:35-40). As in secular life where we must set aside vacation days to rest and focus our attention on family, so in the spiritual life we must set aside holy days to focus our attention more closely on God and neighbor. If left to our own devices, we might never do it. Because the days are set apart ritually, we don’t have to think about doing it because it’s already been done.