She's a legendary figure, but the Romans believed Rhea Silvia was a Vestal virgin, and her sons were Romulus and Remus themselves.

In Silvia's case, she was forced to become a Vestal by her uncle who had usurped her father's throne (of Alba Longa), in an attempt to prevent her from bearing competing claimants. Livy says:

But the Fates had, I believe, already decreed the origin of this great city and the foundation of the mightiest empire under heaven. The Vestal [Rhea] was forcibly violated and gave birth to twins. She named Mars as their father, either because she really believed it, or because the fault might appear less heinous if a deity were the cause of it.

In this case the vestal's children were indeed "given any special/different treatment"-- ...in the sense that they were thrown into the Tiber in an attempt to kill them.

This may not be a particularly satisfying answer to your question, as the Vestal isn't exactly a historical person and Rome herself didn't exist at the time her sons were born, but I'm not aware of any other specific historical Romans who were recorded as having been the children of Vestals.