Not really. From Wikipedia "Having parents who were married by confarreatio was a prerequisite for becoming a Vestal or the Flamen Dialis. Confarreatio seems to have been limited to those whose parents were also married by confarreatio, but later, perhaps with the rise of plebeian nobiles, this requirement must have been relaxed. Scipio Africanus presumably married his wife Aemilia Tertia by confarreatio, because their elder son was Flamen Dialis; yet Scipio's mother Pomponia was a plebeian." That said, Caesar being stripped of the Flamen Dialis position may probably be related to his marriage. The Flamen must be married to a patrician woman. However, Cornelia Cinna has been stripped of citizenship because of the proscription of her father. Even without Sulla, the Senate would not allow the Flamen Dialis to be married to a non Roman citizen. Sulla had two choices: either strip Caesar of his position as Flamen Dialis, based on this legal loophole caused by the Flamina suddenly not being a citizen anymore because of her father's proscription... or to free Caesar from his marriage to Cornelia Cinna based on some other legal loophole (it was not only confarreatio, they were also flamen and flamina, they could not divorce) Sulla chose for Caesar the second option. Let him remain Flamen by divorcing him of Cornelia Cinna and finding another Flamina. Caesar refused to divorce Cornelia. Out of love? Or maybe because that was the ONLY WAY he could stop being a Flamen Dialis? Sulla probably saw that as defiance AND a desire to remain a political ally of Sulla's enemies. BUT the delegation sent by Aurellia to plead for her son probably used the arguments of Caesar desire to stop being Flamen Dialis, a position Marius put him, to try to convince Sulla's to spare the youngster... not a desire to go against Sulla, but a desire to get rid of the position, and remaining married to Cornelia Cinna was the ONLY legal loophole that would allow that.