I find the common use of a crucifix - a tool of torture and execution - to be slightly disturbing in itself. :/
I suppose that the crucifix is probably most appropriate for Good Friday. The cross is for Easter. A star is for Christmas.
The Christmas cards we receive from relatives feature christmas trees, curious george, snowmen, or Santa Claus. Once in a while I get a religious-themed card in the mail from one of my parents siblings, all of whom are over 70. Those rarely feature crosses. They feature a star, or a young couple in a stable with a baby, or three Persians with gifts, or some combination of all those.
I prefer the Elvis-themed Christmas cards. They are pretty rare these days, outside Las Vegas, but they were very common in my youth. I have saved a number of them.