Now that the new Pokemon Home app is announced, players can start bringing Pokemons from their previous games into the new Pokemon Sword and Shield. While this means that you can start battling with your older Pokemons, it also means that players can start breeding new and old Pokemon.
For now, players can only transfer Pokemon that are in the Galar Pokedex but any regional form that takes the same number as the Galar Pokedex will be allowed so you can bring in other forms of Pokemons.
This includes the Alolan Vulpix and Ninetales. To breed more Alolan Vulpix, you will need to give the Pokemon an Everstone to hold before sending it to the Nursery and that will ensure that the parents form will be passed on to the offspring. Do take note that this will only work if the female is the Alolan Pokemon or if you are breeding with Ditto.
This should work for the other alternate forms the are in the Pokedex.