This is a big debate. Some of the major organizations such as ACE and AFAA promote rehearsal movements and dynamic stretching (rhythmic limbering) for a Cardio Warm-Up. Usually short duration static stretches are optional to include and should be performed after the muscles are warm. The research is not 100% at the time. Things to consider as far as including static stretching in the warm up are: type of cardio class, goal of the class and individual, intensity of cardio, type of participants, etc.
I have been teaching for over 25 years and I’m a little old school. I still include some short static stretching (erector spinae, hamstrings, hip flexors, calves) in my all of warm-ups. I includes some static stretching at the end of my post-cardio cool down. I always teach longer duration at the end of the workout.
In my traditional dance and some of my cardio-dance classes, I teach longer static stretching in the warm-up because the workout goal is different from a general population cardio class.
As I can get older and work more with older adults and people with physical disabilities, I believe that flexibility is a very neglected health-related component of physical fitness.