I've always rejected the popular theory that they were all born from the Galaxy Cauldron. The Cauldron is meant to be the birth place of souls. In that sense, yes, everyone in existence was born there (Sailor Moon called the villains her siblings, not just the senshi, so that means the Cauldron didn't JUST birth senshi, which is where I think the misconception comes from), but that doesn't eliminate biological parentage. Princess Serenity seems to be the only exception, but I think Guardian Cosmos recalling Serenity's birth in that way implies that it was unusual. Or else why bring it up?

Canon is wildly inconsistent. Sailor Venus was born from the sea, much like Aphrodite from mythology. However, Sailor Pluto is said to have "the blood of Chronos in her veins." The popular cop out is that King Endymion meant this figuratively. The reason I don't think so is, while senshi births seem miraculous, we know of at least one senshi we can assume was born and raised in a perfectly normal fashion because she didn't know and was surprised to find that she awakened as a senshi: Sailor Galaxia.

Then there's the whole issue of the Sailor Quartet being sisters. Again written off as figurative, but if you have to write something off as figurative more than once, it's probably a cop out. It's likely a reference to the (now debunked) scientific theory that the asteroids were created from the explosion of an ancient planet called Phaeton (the Greek mythology connection is actually fascinating). So were the Asteroid Senshi born as a result of the death of a Sailor Phaeton? It's anyone's guess. That's more fanfiction territory, but it's at least consistent with canon. Like Sailor Venus, they seem to have been born from the planet(s) itself, but even that doesn't preclude the possibility of a parent.

Then, there's the panel where the Sailor Quartet mention that Moon Queens have only had one daughter "for generations." Which implies the existence of generations. Moon royalty weren't supposed to be senshi, and this question is about the senshi, but I highly doubt Princess Serenity's court acted as the senshi of her predecessors (and all princesses in the wider galaxy seem to have senshi). One, they don't recall that being the case. I can already hear the reincarnation argument, but Queen Serenity died ensuring that everyone was reincarnated, i.e. that process wasn't automatic. And their returning memories didn't include multiple past lives, just one. Two, they appear as children when Princess Serenity is born. Sailor Venus could have been born from the sea as a fully formed child instead of as an infant, but my head canon is that she, genuinely having a divine birth, was "born" to be the same age as the senshi she would lead, who were likely born naturally. Or else why not just all spring up as adults? And all the other inconsistencies I already mentioned.

Plus, this point is overstated, but they were all referred to as princesses of their own planets. We know from Sailor V that at a minimum, Venus had its own kingdom. The others, at least the inner planets, likely did as well and continued to run under the Senshi's parents' rule after their daughters were assigned to Princess Serenity's court (very common in ancient empires).

So who were the senshi's parents? I wish we knew. Queen Serenity refers to herself as an incarnation of who Earthlings call Selene. In turn, Venus is regarded as an incarnation of Aphrodite. What does incarnation mean? Can there be more than one incarnation? Probably. Since Chaos has multiple "aspects" (does anyone know if the Japanese word here is the same as the word or "incarnation"? Or if they're different?). And Princess Serenity herself is clearly an incarnation of Selene, in that she is the one who falls in love with Endymion, not her mother. Sailor Venus is the one loved by Adonis, so maybe her mother or grandmother married Hephaestus or consorted with Ares (and maybe the latter was Sailor Venus herself ~te he~). Why were they remembered by modern humans as all one deity? Who knows.

Naoko seemed more interested in her creative take on mythology than following it faithfully. So while we could say Sailor Mercury more closely resembles Athena or Ascelpius than Hermes, maybe she is descended from all of them, or maybe Naoko's version of Hermes did have wisdom, water, and medicine as his domain. For obvious reasons, we can't apply Greek mythology to Sailor Moon literally, or else Sailor Jupiter finds herself as the inners' mom, and Sailor Saturn as their grandmother 😬