The police do not have the legal authority to swipe credit card information without a warrant. The 4th Amendment of the U.S. Constitution protects all citizens from illegal searches and seizures. When a police officer seizes property without a warrant, the government is basically stealing from its citizens. Swiping a credit card without the owner's permission is theft, no matter who does it.
No, cops should not be allowed to swipe credit card information without a warrant. This should be considered a search just as in other search. This is an invasion of privacy for which the cops should have to justify by getting a warrant. Technology should not be allowed to reduce privacy.
A credit card is private. People do not go around giving their credit card numbers out to others. Because of this, cops should need a warrant to access credit card information. However, if they know where someone has used their credit card and can convince the shop to give that information, then this would still be a valid way of bypassing the need for a warrant.
Law enforcement should not be able to obtain anything information that could be used against someone without a warrant. Allowing them to swipe credit card information without a warrant opens up many other options for information to be obtained without a warrant. This directly puts at risk the safety and defense of the subject. It is not something that should be allowed.