Virgin girl needs the permission of her father or her paternal grand father in her marriage.
Non virgin woman does not need her parents' permission in her marriage. Man also does not need permission in his marriage.
If your parents are not happy with your marriage for religious grounds like the person is non Muslim or non believer or non religious etc, you should avoid such marriage. If their disapproval is based on cultural or ethnic or economic reason which are not valid in Islam, you will not be harmed as far as you follow the teachings of the Prophet (SAWA) and Ahlul Bayt (AS).
Wassalam.