Neither of these days is fundamentally religious in character in the United States. They are secular holidays of comparatively recent origin. Besides, in this world, parents are too often forgotten and neglected in day-to-day living, and society attempts to make up for this by a special holiday dedicated to the role of each parent. The Bible, of course, teaches that parents should be honored at all times (Exodus 20:12; Ephesians 6:1-3).
Christians follow God's instructions in remembering and honoring parents. If one also wants to send a card with personal best wishes or to telephone parents on Mother's Day or Father's Day, there is nothing wrong with doing so.