Well, the standard 5.MD.1 simply asks students to convert … it doesn’t say whether they should memorize the relationships. That said, my own opinion is that there are some basic relationships that students should simply know, for example that there are 12 inches in a foot. It seems a waste of time to look this up in a chart when the human brain is already naturally adapted to storing such bits of information. Whether they acquire this by memorization or by repeated exposure is a matter of pedagogy, not specified in the standards. And the metric system is designed for ease of remembering.
Once you have a few basic facts, you can derive the others. For example, if you know there are 100 centimeters in a meter, you also know that a centimeter is 0.01 meters; it is not a separate fact, but a related fact coming from and understanding of the relationship between multiplication and division and an understanding of decimal notation.