I think one of the rather biggest misconceptions about Power Ranger cast changes, especially during the Zordon Era, is that they're all unpopular. This is not always the case.
The first Power Ranger cast change during MMPR S2 saw the departure of Jason, Trini, and Zack because their respective actors all left the set because their salary demands were not met. All three of them were very popular rangers, but that did not stunt the show's popularity. In fact MMPR S2's ratings were higher than S1, which in turn led to the movie being released during the summer of 1995, which did quite well. Some of the new cast members, particularly Aisha and Rocky, aren't exactly popular characters. This is partly due to the poor character development that these two recieved, the fact that they were overshadowed by Jason and Trini, and also partly because for a long time the actor who played Rocky, Steve Cardenas, wanted nothing to do with Power Rangers. Cardenas would later change and has regularly been coming to Power Ranger conventions. Adam, on the other hand, is generally well liked by most PR fans from from all fan bases (MMPR, Zordon Era, Post Zordon Era, exc). In recent years, Adam has become more popular than Zack.
Power Rangers Turbo had one of the most unpopular cast changes as well as one of the most popular cast changes during Power Rangers history. Rocky, a rather so-so character was replaced by an even less popular ranger, Justin. At the time, Fox Kids basically forced Saban to cast a kid on the Power Rangers set because they wanted to appeal to Power Rangers' kid's fanbase. What Fox Kids didn't realize was that by this time, the show was already five years old and the fanbase was getting older. The majority of Power Ranger fans during Turbo and even now berate Justin not only because he was a kid, but because he acted like an immature kid. This went heavily against the show's tradition of teenagers with attitude.
On the other hand, the cast change during the second half of Turbo is misconceived by some to be unpopular and what ruined the show. The truth is that while some PR fans didn't like the cast change, most loved the cast change. Immediately after the cast change, Turbo's dwindling ratings went up which saved the show from cancellation. Ashley and Carlos were already present during the first half of the show, while TJ and Cassie were introduced just before the change and went on to become popular characters. The second half of Turbo was also helped by the change of writers with Judd Lynn taking control.
While not initially as unpopular during Lost Galaxy, because Lost Galaxy still had many Zordon Era connections, the cast change as well as the changing theme every year was rather unpopular in Lightspeed Rescue. It didn't help much in Lightspeed Rescue that it had a rather so-so cast. However, Power Rangers Time Force excited many fans with a rather likable cast, and by this time most PR fans understood more about Sentai and were over the continually changing cast from year to year.