As this section relates to the restoration of the monarchy, and succession to the headship of the house of Savoy, it is however interesting to lay out the things we know, despite a seeming mountain to climb before an Italian kingdom is again proclaimed. Unfortunately, as has been so clearly illustrated by recent years history, and a large number of posts in the Italian section of these forums, the fight for the headship of the family overshadows the cause itself. In all fairness, if one excludes the possibility of a monarchical restoration, I don't see the problem letting the branches disagree, and split, like happens in any family in the world from time to time. At some point in the future, feuding families tend to reconcile on their own. If not, the current rules of headship indicate that in a future decades away, headship of the House of Savoy will transfer to the Duke of Aosta and his branch.
For now, Italy still has a former Crown Prince, who himself has a son, who himself has two daughters. Whether one approves or not, that is the last recognised resemblance of an Italian Royal Family.
The questions to follow is whether dynastic approval for the Crown Princes marriage was given, and whether succession would be changed to accommodate girls. This is the basis for a circular debate that frankly interests very few people, and is neither helpful, nor practically resolvable in the current Italian republic. What remains then is supporters deadlocked in positions I'm sure they feel they can validate in one direction or another, but that is seldom explained based on facts, but rather on personal taste and preference, i.e references to the Prince of Venice and Piedmont as 'that dancing dude' etc.
I always find it interesting that many people seem more interested in supporting a person than a cause. That is one of the reasons monarchies often fail, and why it is hard to restore them once they're taken down, if we link them so firmly to one person, and not as a way of organizing societies. The institution should be bigger than the person, as proven by King Juan Carlos in 2014, by abdicating the throne of Spain in favour of his successor.
As is extensively explained at
Headship of the House of Savoy - Savoy Succession Dispute - Vittorio Emanuele di Savoia - Victor Emmanuel of Savoy - Amedeo di Savoia Aosta - Amadeus Savoy - Head of the House of Savoy of Italy - Regalis - Savoy Succession, headship of the House of Savoy lies with the Crown Prince, then the Prince of Venice, before it will cross to the Duke of Aosta and their family. That is, unless something new were to arise in the 40-50 years ahead. Looking at the history, and the unpredictabilty of future events, it would seem silly to sit idly by and wait for a transfer of headship upon the demise of the current Prince, time that might be better spent advocating the cause of monarchy, in a nation that was once a proud kingdom, and which is being abused by generations of politicians, who could do with a bit of a political shake-up, and a new order to their chaotic existence.
Finally, I would just add that whatever the future holds for the Italian Royal Family, and whatever they have done in the past, neither of these two men, the Crown Prince and the Duke of Aosta, are very fine examples of moral restraint, and their failings over the years is evident in courtcases, illegitimate children etc. I would hope that any future monarchy, or even just a more healthy House of Savoy, would be allowed to be based on love-based unions and peaceful solutions to conflict. That would greatly benefit the family itself, their representation of Italian history and any prospects of a future Italian kingdom.