What is being tested
People's opinion can be shaped by what is being tested. For instance few if any would find animal testing wrong when testing animal food (Dog food for instance) as a taste test. Testing a cosmetic for skin rashes, hair loss, hair color change, is another one.
The need for the testing
Certain testing may not be necessary at all. Necessary testing, for instance, safety has a high degree of acceptability then purely speculative research. A great example was a test in the 1990 on how long they could keep a severed dog head alive. The necessity of that kind of a test was unacceptable to quite a few people where as testing an insulin medication on a diabetic dog prior to a human would have fewer opponents then the previous example.
The impact to the animal
This is the easiest to understand and the most reactionary. Regardless of the previous criteria most animals do not get a say in their use. Thus they cannot be complacent in their use. Testing hair coloring on a dog may give them blue fur for a few months but the impact is minimal to the dog. If the hair coloring causes blisters and pain to the animal the degree of acceptability is greatly reduced as the dog had not say and could not possible understand the potential pain and suffering. Worse yet for the animal is many tests require the termination of the animal for post-mortem study. This is especially difficult to accept with animals that are normally pets (dogs and cats for instance.)
The Cute Factor
Yes the cuter the animal the harder it is to accept testing. You can get away with dissecting a frog in a school but you would be hard pressed to disect a cat or ferret.
While the opinions can vary based on a broad canvas of critiera the above tends to be the most recognizable factors in the contraversy.