Is it permissible to boycott one's brother and refuse to go with him to propose to a girl who does not adhere to Islamic guidelines, and what is the ruling of Sharia on the parents' insistence on completing this engagement despite their knowledge of their son's misconduct and indebtedness, and what should they do now?

There is no objection to refraining from going with a brother who is disobedient to his Lord and violates His law. Rather, it is obligatory to refrain from accompanying him in what violates the Shari'ah so that you do not become an aid to him in his disobedience. It is permissible to shun relatives who persist in sins.

However, if he requests something permissible, it is preferable to respond with the intention of winning his heart and inclining him towards good.

His parents are not obligated to spend on him if he is able to earn a living but does not work. It is also not permissible to give him money if he will use it to commit acts of disobedience.

Your duty is to advise him, remind him, admonish him, and pray for him. If he persists in his sins, then you are not responsible for anything after fulfilling the duty of advice. Beware of being an aid to him in his disobedience, and take a stand of disapproval towards his actions so that it may deter him.