Is giving gifts to family members on Eid al-Fitr and Eid al-Adha and consistently doing so annually considered an innovation (bid‘ah)?

There is no harm in exchanging gifts on Eid al-Fitr and Eid al-Adha, for these are days of joy, happiness, and kinship. This is considered a good custom among the rituals of Eid, unlike innovated days such as New Year, the Mawlid (Prophet's birthday), or the 15th of Sha'ban, on which it is not permissible to show joy or exchange gifts.

Sheikh Ibn Uthaymeen said: "The Sharia, praise be to Allah, in its facilitation and ease for His servants, has opened for them a measure of joy and happiness on the days of Eid."