There's nothing inherently wrong with modifying more than one private variable in your setter. The variable names in your example lack any useful meaning or context so I can only guess at what this is about. Based on the fact that you are adding the name of the property ("abc") to the 'string list', I figure this is some sort of observable pattern implementation. Nothing wrong with that, in itself.
There is a major issue with this class, however. It's that you have a getter and setter for a list. This is a terrible, terrible approach. One part of the code can call the getter for the list and be able to see all the "abc" strings you are adding to it and starting adding their own values such as "butt" and "poop" (or any object really) but only up until some other part of the program replaces the list object that your object is using internally with their own list. This is a tremendously egregious breaking of encapsulation. It will definitely be a debugging nightmare. Did I mention that this is a terrible approach?
You should never ever return or accept a collection or array in a setter. Returning a modifiable collection or array from a getter is also a big mistake. If you give a little more context to what you are trying to accomplish, I will offer some alternative approaches.
Here's a little code to demonstrate how your current code behaves. I added a print to setAbc that counts the calls to help make it more clear what is happening:
final Thisismyclass instance = new Thisismyclass();
ArrayList<String> listA = instance.getStringList();
ArrayList<String> listB = instance.getStringList();
System.out.println();
System.out.println("listA: " + listA);
System.out.println("listB: " + listB);
instance.setStringList(listB);
ArrayList<String> listC = instance.getStringList();
System.out.println();
System.out.println("listA is same as listB? " + (listA == listB));
System.out.println("listB is same as listC? " + (listB == listC));
listB.add("yipee!");
instance.setAbc(true);
System.out.println();
System.out.println("listA: " + listA);
System.out.println("listB: " + listB);
System.out.println("listC: " + listC);
instance.setStringList(null); // HA HA!
instance.setAbc(true);
ArrayList<String> listD = instance.getStringList();
System.out.println();
System.out.println("listA: " + listA);
System.out.println("listB: " + listB);
System.out.println("listC: " + listC);
System.out.println("listD: " + listD);
System.out.println();
System.out.println("listD is same as listA? " + (listD == listA));
System.out.println("listD is same as listB? " + (listD == listB));
System.out.println("listD is same as listC? " + (listD == listC));
System.out.println();
System.out.println("listA: " + listA);
System.out.println("listB: " + listB);
System.out.println("listC: " + listC);
System.out.println("listD: " + listD);
instance.setAbc(true);
System.out.println();
System.out.println("listA: " + listA);
System.out.println("listB: " + listB);
System.out.println("listC: " + listC);
System.out.println("listD: " + listD);
ArrayList<String> listE = instance.getStringList();
ArrayList<String> listF = instance.getStringList();
listE.add("nananananananananana Batman!");
System.out.println();
System.out.println("listA: " + listA);
System.out.println("listB: " + listB);
System.out.println("listC: " + listC);
System.out.println("listD: " + listD);
System.out.println("listE: " + listE);
System.out.println("listF: " + listF);
instance.setAbc(true);
System.out.println();
System.out.println("listA: " + listA);
System.out.println("listB: " + listB);
System.out.println("listC: " + listC);
System.out.println("listD: " + listD);
System.out.println("listE: " + listE);
System.out.println("listF: " + listF);
instance.setStringList(listE);
ArrayList<String> listG = instance.getStringList();
System.out.println();
System.out.println("listA: " + listA);
System.out.println("listB: " + listB);
System.out.println("listC: " + listC);
System.out.println("listD: " + listD);
System.out.println("listE: " + listE);
System.out.println("listF: " + listF);
System.out.println("listG: " + listG);
instance.setAbc(true);
System.out.println();
System.out.println("listA: " + listA);
System.out.println("listB: " + listB);
System.out.println("listC: " + listC);
System.out.println("listD: " + listD);
System.out.println("listE: " + listE);
System.out.println("listF: " + listF);
System.out.println("listG: " + listG);