I know your parents do not live in Shanghai.
But why did you say they are not living in Shanghai?
What did you want to imply by adopting the present continuous tense?

One can say: my parents are living in Shanghai.
But it sounds just so strange to make an introduction
by saying ‘my parents are NOT living in Shanghai',
especially when her parents actually never lived in
Shanghai. The simple present tense would make more sense
to me.

哈哈