If the parents are paying for the wedding, then they should have some say. If the parents are going to fully support them, then they should have a lot of say.
No, they should not. They certainly should be free to refuse to pay for (and provide long-term support for) a wedding they don’t approve of, but they don’t get an automatic veto just because they are paying. The only veto they get is on their wallets.
The Wolf