Reading D&C 29:34 we understand that even laws that appear to be temporal laws, such as the word of wisdom, are really meant to have spiritual implications. The word of wisdom and others like it are laws that are designed to help keep us free of obstacles or distractions in feeling of the spirit. For the word of wisdom, its key promise is strength to our body and minds and for us to be given wisdom and treasures of knowledge even hidden treasures. Or in other words, do not partake of things that will cause our faculties to judge righteously to be diminished or destroyed, or that will shut us off from the spirit. The word of wisdom also counsels against partaking of items that are addictive and enslaving. Sin is no respecter of person, and therefore no exceptions should be made to these laws including the person saying, "I can keep it under control-that rule doesn't apply to me because I can handle myself and won't get addicted". Such a rationalization is a lie of the adversary meant to lull the individual into a sense of complacency with sin.
While credit cards seem to have no attachment to the word of wisdom (unless you are eating them for roughage), there are principles that coincide with the counsels of warning similar to those in the word of wisdom. As coffee and tea are readily available and carry no age restrictions for consumption, many in the world consume coffee at very early ages. This consumption creates an environment of people that "can't start their day without a cup of coffee". To that end I have seen some start their lives so young with credit cards and unnecessary spending that the credit balances are rarely caught up or erased.
It is easy for a person with a credit card to rationalize the use of the card as an emergency use only, to build their credit, etc. However, the brethren have been as clear on this issue as they have on coffee and tea which could also have a rationalized benefit should you chose to see it that way. With debit, we are counseled to avoid unnecessary debt (necessary debt being defined as a house, a reasonable car, and for your education), don't become in bondage to creditors, engage in a prudent savings plan, and live within your means. Credit cards are living outside of your means, it eats up savings, and is a debt that carries an enslaving high interest rate-all in direct violation of the counsel of the brethren. If wise counsel is followed, then credit cards are not needed and the individual can avoid the bondage that is sure to follow.
Have you ever noticed that the church does not accept credit cards for tithing as many other faiths have done? Is this because the church couldn't set that up? Of course they could. And there is a very clear reason why they probably won't ever take credit cards for tithing or fast offerings. So if the above is true, that credit can be seen as an addictive practice that will consume the individual with worldly interests, then why have one to begin with? Why have a coffee maker and a can of coffee grounds if you know you shouldn't drink it? If you have a credit card will that dismiss the spirit-of course not. But having the credit card leads to using the credit card, and using the credit card leads to nothing good and wise and to practices that diminish our capacity to feel and recognize the promptings of the spirit.