You can think of a small card in someone's wallet with their name and an organization on it. Anyone can say they are on your side; this person can reach into a pocket and show it. That act of proof is what the word carries. Once the picture is clear, English uses it on people who have no card at all — the card becomes a way of saying there is no doubt about this one.
One branch
拿得出卡的人
兩個意思都靠同一個動作：掏出卡來。一個是真的有卡，一個是借這個畫面來說「毫無疑問」。
adjective · C1
Used in 'card-carrying member' to describe someone who has paid to join a political party or a similar organization and is an official, active member of it, not just a supporter who agrees with it.
正式入黨（入會）的成員