Some of the Red Cross classes are OK, and some are surely not, unless you are purely a city-dweller with emergency services available. For most of us who backpack, the "mountain medicine" classes are much better.
I took a basic Red Cross first aid class one time, and it was bad. The instructor did not understand hypothermia or altitude illness or any of those "mountain" subjects and was unprepared to teach those topics. So, it is good to get into the correct level of class that really works for you. As a general rule, the Sierra Club has links to those kinds of "mountain" first aid classes.
About 25 years ago, the Sierra Club had some ugly accidents on sponsored trips, and there were lawsuits. In order for the Sierra Club to be able to continue its operations and its liability insurance, it had to increase its leader training significantly. So, for the last 20 years or so, the accident rate is much lower and the accident management is much better.