If I remember correctly it was less to do with the cards themselves and more to do with the environment that playing cards can create.

I think it is stupid.

I believe the clean shaved look was because David O McKay was the first modern day prophet to be clean shaven and before that when people thought of Mormons they thought of long bearded old men. President McKay reshaped this image and brought the church into the mainstream. Not sure why you can't be a bishop and have facial hair though. There no doctrine behind it. I did find this quote about it

'"In February 1993, the LDS church posted an article in its Ensign magazine stating, "Church leaders, recognizing that fashions go in cycles, are sensitive to the rich cultural diversity within the Church. For example, they have recently held that clean, neatly trimmed and managed beards …are acceptable for the temple, provided they are not inherently offensive or vulgar."[vii] However, by 2001 being clean-shaven "became policy for those who work regularly in LDS temples."[viii]"'