Yes mustard can eventually stain some peoples teeth if you do not brush your teeth after eating mustard on foods.
As long as you brush your teeth properly after eating the mustard then the mustard should not stain your teeth but if you do not brush your teeth after eating mustard then your teeth can be stained.
I've never had a problem with mustard staining my teeth since I always brush my teeth after eating mustard and at every meal.
So it's not a problem for me but your teeth can be stained from mustard as well as other foods such as ketchup, tomato sauce etc.
If you do get mustard stains on your teeth then you can use some baking soda and water to brush your teeth with and use some teeth whitening strips to help get rid of the mustard stains on your teeth.