I'll just repeat what somebody else said:
The Vinsmokes are an underground organization that are probably often hired by the celestial dragons and/or the Gorosei. The Cipher Pols are a really important organization inside the World Government, but they also are responsible for doing intel work, like collecting information, and dealing with stuff that is not exactly suited for the marines (Dragon mentioned them, talking about how strong they got, so they're probably a problem for the Revs).
That being said, there are a lot of celestial dragons out there, and they surely like to kill people. If the Gorosei had to dispatch an Admiral or Cipher Pol member everytime a celestial dragon wanted somebody dead then all of the intel work the Cipher Pols are doing would have to be halted/compromised. It's not too far-fetched to think that the Gorosei would rather employ some other solution, and this solution could very well be a family of underground assassins. Keep in mind that giving a lot of money to an underground assassin's group wouldn't be a problem for the World Government.
Now, it's not too far-fetched to think such an organization would have some level of influence over the World Government. Look at Doflamingo, for example. He managed to manipulate the News and request both an admiral and the CP0 to help him. Given the importance the Vinsmoke family could have for the WG then they could have some good influence over them. Anything like "Each scratch you put on him will result a dead celestial dragon" or "Either you do that or the entire world will know you're paying an underground assassination organization" would be more than enough to change Sanji's wanted poster.
For me if the Vinsmokes were the CP0 or under the WG in any form then they likely would have a lot less power and influence. That doesn't rule out the fact that they could cooperate, though.
Sorry for the lenghty post! Tl;Dr: The Vinsmokes are important for the World Govermnent, but indepedent of them. They likely conduct assassinations for the Celestial Dragons and the Gorosei, and as such have some sort of influence over them, enough to force then to change Sanji's wanted poster.