Are parents entitled to demand a large dowry ($50,000) from a young man who is very religious and of good character?

There is no minimum or maximum limit for the mahr (dower), and the Sunnah (definition) is to keep it small and easy. If the woman and her guardian differ in determining the mahr, then for a virgin, the guardian's word is considered if the mahr is less than the mahr of her peers, and her word is considered if the mahr is equal to or more than the mahr of her peers. As for the previously married woman (al-Ayyim/Thayyib), her consent is what matters, and her guardian's consent is not regarded.