Is it permissible for a Muslim man to go out with one of his mahrams, such as his mother or sister, if she does not adhere to the Islamic dress code (unveiled face, wearing a tight abaya or clothing that has adornments)?

A distinction should be made between uncovering the face and other forms of tabarruj (displaying one's adornment). The disagreement regarding uncovering the face is a valid one, and there is no sin upon a mahram (unmarriageable kin) for going out with his mahram who uncovers her face, in imitation of those who permitted it, provided that the rest of her attire conforms to the Islamic guidelines. However, if her attire violates the Islamic specifications, then it is not permissible for her guardian to allow her to go out in such a state, nor is it permissible for any of her mahrams to go out with her in that condition.