Why do the pirates have white teeth?

This was discussed in an interview with the show's creator Zach MacGowan. He's offered a number of in-universe and out-of-universe answers to your question:

Out-of-Universe reasons:

• Most actors have nice teeth
• Prosthetic teeth are expensive
• Prosthetic teeth are time-consuming to fit
• Prosthetic teeth impede speech
• They've actually experimented with teeth-yellowing paint but it rubs off after a few hours

In-universe reason:

• There must be some pirates who had good teeth. We just happen to have come across quite a few of them.

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Legion of Leia: When we were down there, one of the cool things that we learned was that a bunch of pirate experts watch the show and the only thing that isn’t historically accurate is the white teeth! Have you done research on pirate history for the role?

Zach McGowan: Yeah, I have. What’s interesting about the white teeth argument is, a lot of us actually have put paint on the teeth to get them yellow. It’s just the nature of the shoot is such that when we actually get out on the set sometimes the upkeep of that can be difficult. Obviously it’s in your mouth and the saliva ends up bringing it out. It becomes a very difficult thing to do without doing mouth prosthetics, which, you know, the show has a lot of stuff going on already. It also affects the actor’s ability to speak. There is a lot of dialogue on the show. I mean, we don’t think about it all that much. I mean, I have to say that personally, I’ve never had anything done to my teeth. [laughs] I don’t go to a dentist to – I mean, I do brush my teeth, which those guys did not do, of course. But it’s not like I got braces and tooth whitening for the show or anything like that. I happen to be blessed with pretty good teeth from my parents. There must have been a few pirates out there with good teeth! Early on, a lot of us were pushing for gold teeth and things like that, but I think decisions to not do things like that were based on things like, we met these pirates and they weren’t rich. They didn’t have a lot of gold. In Season 1, you don’t see any gold. It took this seizing of the [Urca] gold to infuse the culture with that a bit more. What did I learn? I learned so much about pirate culture that I didn’t know. It seems like most of it came out of necessity. And that it was a very hard life and people did what they needed to to survive.