Granted, as kids, we didn't notice much. All we cared about was making sure Cory and Topanga stayed together forever. Adults had little impact on that story. It wasn't until we were older, rewatching the best show ever, Boy Meets World, that we realized Topanga was either a foster kid or constantly being adopted by other people. We never knew she had such a hard, changing life. Kids need stability! Maybe they tried to offer that stability by taking the names of the original parents? Or, the plot thickens. Maybe Topanga was a part of a cult—it's all starting to add up now.
Peter Tork was replaced by Michael McKean, who was replaced by Mark Harelik as the father, Jedidiah Lawrence. Three different dads, Topanga? Damn. We can only guess that, since they were such minor characters, it didn't really matter. The actors were probably off trying to do other things in their career, like Peter Tork who was the Monkees bassist—he was probably busy.
Annette O'Toole was replaced by Marcia Cross as Rhiannon Lawrence, Topanga's mom, and we don't really know why. But Boy Meets World isn't highly regarded for its continuity. In fact, Topanga used to say her mom's name was "Chloe" in the early seasons, not Rhiannon. Do your research on your own show, writers.