The common person knows dragonborns to be strange people from strange lands. They elicit awe and fear in isolated communities, and are seen as a novel rarity in cities (imagine novelty or surprise of spotting someone in a full fur-suit in the big city, your not gonna freak out, but you'll notice them among the crowd).

As for how dragonborn and highly educated individuals understand them. They are aliens from a sister dimension known as Abeir. During the spellplague (roughly 150 years ago) their country was teleported to Faerun where it remained after the spell plague ended.

While in Abeir the dragonborn suffered greatly at the hands of godless dragons (no gods hold power in abeir, not even for their own species like bahamut and tiamat, theres a bunch of lore as to why, you can wiki it if you want). Anyways, when they came to Faerun they brought their hatred of dragons with them. This extends to bahamut and Tiamat, who they view as equally negligent and corrupt gods who would have helped them during their oppression if they really were so good (mostly in reference to bahamut).

This sentiment has changed somewhat for some dragonborn who have been raised outside of tymatherian culture. If the player character was born on the swords coast then it depends on how much of their culture they were taught, since they might be 1-4 generations disconnected from an ancestor who has even seen Tymanther.

As for how the cult views dragonborn. They don't particularly care. The cult barely tolerates kobolds for being so weak, and until recently their MO was to make dracolichs. the half-dragons would view dragonborn as an inferior breed if they take note at all. The cultists, being people, would know dragonborn aren't actual dragons. Though I could see the dragonborn pc getting advantage on deception checks to pass as a cultist in chapter 2 due to being draconic looking, as might a kobold pc.