Some forms of Mucinex, like Mucinex D, contain pseudoephedrine, which can decrease milk supply1 in some people. So it might not be the best choice if you're trying to maintain or increase your milk supply.
However, plain Mucinex (Mucinex Guaifenesin) without additional active ingredients is generally considered safe2 . It's always a smart idea to take medications as directed, and if possible, time it so that you're taking it right after you've finished nursing.
As always, your healthcare provider is your go-to resource for personalized advice. So don't hesitate to reach out to them with any questions you may have.
Remember, taking care of yourself is an important part of taking care of your baby.