I believe that the parents of Celestia and Luna could not be alicorns or rulers of Equestria. Because judging by the history of season 8, Celestia and Luna were originally ordinary unicorns, and accidentally discovered the ability to control the sun and the moon without losing magic. Then they became alicorns and rulers of Equestria, thanks to Starswirl. Therefore, I think that their parents were also ordinary unicorns.
 
This is how I imagine them:
 
Stargazer (father) is a famous astrologer and astronomer who has dedicated his entire life to the study of the cosmos. Lily (mother) is a pony from a wealthy family, a dreamer who loves night walks through the forest. They met just at one of these walks, when Stargazer looked at the constellation through a telescope in the forest, and Lily accidentally stumbled upon him and decided to join.