If judges are supposed to be strict interpreters of the constitution, why do you think the decision of who sits on the supreme court is so important?

The easiest way to summarize the importance is to give you this scenario:

What is a reasonable amount of butter to put on popcorn at the movie theatre?

I can almost guarantee you that our definitions of what is reasonable will differ. Our goals likely differ as well. You may be on a date and don't want to have hands covered in butter. I may be going to see a movie alone and don't care how gross I look.

Judges on the Supreme Court approach law in the same way. They differ in what they view as reasonable but they also differ in what their goals for the law are as they have had different life experiences that have gotten them to the point where they are Judges.

So, while all Judges are supposed to faithfully interpret the Constitution, they do so with different goals and different measuring sticks for what is reasonable. As a result, they will appeal to different groups.