Yes, I think in many cases, it happens. Basically, we still have conservative atmosphere in families. People say they are modern but one should be first modern and open in thinking and thereafter in other matters like clothes n all. Actually parents forget that they have also gone through the same phase in their childhood or adolescent age. If parents will listen carefully and discuss the issue properly then children will find a good friend in parents and that will be a superb equation. Nobody than parents can better understand and suggest solution for any problem or issue.
I think children should also know their parents as to how, when and in which manner the issue should be discussed with parents.
One more thing, the issue can be discussed in presence of such person who matters to your parents, who can convince them. Also, if something is refused or said otherwise by parents then children should also give a second thought about what they are saying.
If parents stick to their opinion then children should calmly discuss the issue step by step and make them aware of present day circumstances with all the positive points. Parents are always bothered about safety of their children so child should convey from that aspect also.
Whatever the outcome may be, children should discuss each n every issue with their parents as nobody else is as great well wisher of a child than his/her parents. Do not lose hope and keep trying to make them understand your view point. Keep patience and try to make them understand from another angle.