I think one of our other historians would probably be better at explaining the view of sexuality during this period - but I'll say two things.

One, for pirates, there is no documentation saying that homosexuality was something of note among pirates. There is no evidence that pirates differed from the general public on the matter of sexuality. There is also no reason to believe there would be differentiation on this matter.
Two, sexual identity was a completely different thing compared to late 20th/early 21st century conceptions of sexuality. Based on what I've read in Michael McKeon's The Secret History of Domesticity: Public, Private, and the Division of Knowledge, they didn't view identity as homosexual or heterosexual or other labels like we do today. They didn't identify themselves by sexuality at the scale people do today. So there's a whole factor that makes it difficult to compare today to back then.

Basically, the way "Black Sails" presents sexuality in a nowhere near accurate manner. It would be considered highly exceptional and surprising to see the kind of sexuality presented on that show during the actual Golden Age of Piracy. Much of what "Black Sails" does is an appeal to audiences in the typical Hollywood way.

For period perspectives on sexuality, I'm pretty sure we have a historian for that subject around here somewhere and have a selection on the FAQ for this subreddit that can also help you out.

So I'm here to provide the compliment to /u/davidAOP's post. I know rather little about piracy, but rather a lot about the history of sexuality.
davidAOP is correct in asserting that historical understandings of sex and sexuality differed significantly from our own. There have been significant shifts over time in how societies have understood sex, gender, and what we now call sexual orientation. The concept of "homosexuality" (and as such, "heterosexuality) simply did not exist prior to the mid 19th century (and didn't really become fully cemented as discrete identities until the mid 20th.)
This obviously makes the study of historical sexuality somewhat complicated. Whereas today we center the difference around who you sleep with (someone of the opposite gender or someone of the same) earlier times in (Western) history the difference was centered a little more on how you slept with someone and how you both conceived of your gender identity. That is to say one's role in sex (and how that role was gendered) was more important than who one was getting busy with (as the kids say.) So a man taking the penetrative role in sex was considered normal, proper, and masculine , with little regard to the gender of his partner. The receptive sex role was considered appropriate for women, boys, or effeminate men called at various times "mollies," "fairies," and "pansies." It isn't until later that men began to conceive of same-sex attraction (outside of these very gendered systems) as being a central part of identity.
And well, as to lesbians and female same-sex relationships, they certainly existed, but of course we have exceedingly little record. The issue of private vs. public comes into play even more, as women were largely confined to the sphere of the home.
That is all a very preliminary and slightly over-simplified take on history of sexuality and how it differs from modern understandings. I am happy to answer follow-up questions.

That's a very difficult question and would probably require some significant research before it can be adressed properly. The thesis put forward by Thomas Laqueur is a very popular one, despite some criticism, it's still a very convincing theory. In his work on the history of sexuality, Laqueur claims that before the 18th century there was no such thing as a "two-sex theory" and in fact the "one-sex theory" was what defined notions of sexuality. In this "one-sex theory", a woman was simply an underdeveloped man. However, gender and sex were not synonymous in this world view. Someone who was biologically a woman would sometimes be considered as "respectable" as a man if she acted as a man should. She was then defined by her perceived gender, not by her sex. The strength of this thesis lies in the fact that it explains the common thought that women were able to "overcome" their nature - being underdeveloped. Biological determinism wasn't as extreme as it has been in more recent times. One might criticize this theory by pointing out the complete lack of matriarchal societies in history. However, I don't think that's relevant criticism. Biological inclinations and expectations might have not been adressed, but that doesn't mean they didn't exist. If tradition and common practice expected certain things from a woman based on these biological inclinations, acting differently would upset this pattern and cause friction. This does not imply biological determinism.

When talking about this specific casus, I'd assume that this series takes place in the early 18th century? When we go by the thesis of Thomas Laqueur, it's safe to say that popular thought was still defined by "the one-sex theory". At this point in time, there wasn't such a clear-cut division between homosexuality and heterosexuality based on sex. So same-sex relations might still be considered 'unorthodox', but would most likely only ellicit responses based on gender behaviour. If one of the partners in this relationship would exhibit behaviour that could identify him as 'feminine', his peers would most likely think less of him. Not because he was homosexual, but because he didn't act like a man should. Again, this is all very much up for debate and it would require some intensive research to properly adress this issue.