Mindfulness is definitely not meant to suppress thought or even certain types of thought. At its core it is non-judgmental observation of arising mental phenome

Mindfulness is definitely not meant to suppress thought or even certain types of thought. At its core it is non-judgmental observation of arising mental phenomena. That means thought, emotion, perception (e.g. touch), and even consciousness as observables, without any type of internal labeling ('that's a bad thought, that's a bad emotion, etc.'). It's possible for people to fall into this, where they exclusively focus on concentration meditation (like the breath) that leads to a kind of narrow-mindedness. It's also difficult because there are just so many books out there for people to read, that it's tough to know exactly what people are reading and suggesting to others, and some of the new-agey type literature ('think positive!') can possibly be harmful. There are many reputable sources (historically and currently) that can say that the purpose is NOT to suppress your thoughts, even though this can be a common misconception about meditation practice.