Joseph,
Should parents have a veto?
No, it’s not their life.
Should they be making the selection for their child to approve of?
That depends on what the child and parents want, and the norms of their community.
Should they have absolutely no input if their child is deadset on marrying a specific person?
What do you mean input? Of course parents should advise their children and raise concerns if needed. They should also be aware that their children may make different decisions than they would, and how the parents react to those decisions can impact the relationship with their child/prospective new in-law.
Is it different whether the child is a son or daughter?
Why would it be?