TL;DR - Among those pirate crews that sailed the Atlantic world during the late 17th and early 18th century, black men were present, but their status among the pirates is questionable. I have one account of a generic "Indian" for American Indians among these groups.

First, the easier topic - black men in pirate crews.
The story that floats around in the public is that pirate ships are places of democracy and freedom for black men. They were supposedly allowed freedom to join the pirates and be treated as equal crewmembers with votes and everything. Some of that came from particular people pushing the idea so they could promote piracy with more moral justification in the early 1990s. But if one goes back and examines the documents concerning this more closely, the picture is much more blurred and gray.

Pirates were mostly former sailors of European descent. There is no reason or evidence that they changed their views on racial issues that drastically when they became pirates. Black men who were on slave ships heading to the new world were more likely to find themselves remaining as property after pirates took their ship. Either they might be kept by the pirates to be used as forced labor on the ship for menial tasks and/or sold and traded at the first opportunity for the crew's profit. The odds of them having maritime skills was low and they are extremely unlikely to speak a language that the crew did. As a result, it's highly unlikely they would become part of the crew, and records after slave ships were attack demonstrate this. What is worse, on a couple of occasions, slaves in chains below decks were not unlocked before pirates trying to quickly get out of an area before being pursued by authorities resulted in slaves being burned alive on ships the pirates decided to burn. Other pirates also came into direct conflict with Africans in their homeland when pirates came to shore. One incident resulted in the destruction of a African village by pirates.

Meanwhile, there are some that may have received better or close onto equal treatment. One instance that comes to mind to demonstrate that a black man was treated equal was a description of work distribution on Captain Stede Bonnet's crew. It appears that those black men that had made it over the middle passage, picked up maritime skills, and could speak a language the pirates could understand had a much better chance at better treatment, or possibly equal treatment. In a lot of pirate crews, clarity is never given as to who had voting rights. Plenty of crews show that not all white members had voting rights (in particular, forced men and brand new volunteers to the crew). I should note, there isn't a terrible amount of evidence that every pirate crew had voting rights at all. You can document about a quarter of them voting in their captain, and that's about it. Anyway, back to the topic at hand. It would be a concerning question to these black men on a ship on whether, if it became convenient, would they all of a sudden be seized up and sold for the profit of the rest of the white pirate crew. White men had done it before, other pirate crews did it before, why not them? Black men are even recorded fighting against pirates who took their ship. In one case in the Caribbean, black pearl divers had the ship they were on captured. The black pearl divers helped the former owners retake the ship from the pirates in a fight.

Two good sources concerning black men and pirates during the Golden Age of Piracy are a pair of articles by Arne Bialuschewski entitled “Pirates, Black Sailors and Seafaring Slaves in the Anglo-American Maritime World , 1716-1726.” The Journal of Caribbean History 2, no. 45 (2011): 143–158 and “Black People under the Black Flag: Piracy and the Slave Trade on the West Coast of Africa, 1718–1723.” Slavery & Abolition 29, no. 4 (December 2008): 461–475. One note, Bialuschewski does take a harder approach to the subject and is somewhat "all or none" in his approach, and probably could leave more gray area in his work.

As for the one Indian I know of - there is John Julian of Samuel Bellamy's pirate crew (which mostly sank off the coast of Cape Cod in 1717). He is listed as a "Indian" on several occasions, and just one document more than likely lists him as a "Moskito Indian" meaning a native of the Mosquito Coast of Nicaragua - this has never really been verified. Also, there is no verified relation that he is the same "Julian the Indian" that is hanged about a decade later and owned by John Adam's (yes, founding father John Adams) father.

Jane Landers notes in her chapter entitled “Transforming Bondsmen into Vassals: Arming Slaves in Colonial Spanish America.” in Christopher Leslie Brown and Philip D. Morgan, eds., Arming Slaves, From Classical Times to the Modern Age, that a former African slave by the name of Diego Martin had become a successful pirate captain working at times for the Dutch West India Company. Interestingly enough, in 1638, Martin was given a royal commission by the Spanish and defended his place of enslavement, Cuba, from the Dutch. In part due to his success as a corsair, the Spanish gave Martin a large salary, equivalent to that of an admiral to fight for them.

Hi there, It has been stipulated that because the Pirate community was somewhat of a democracy (i.e leaders, captain's and commodores were elected by popular vote), Native American's and African Slaves were not only pirates, but they could have potentially been Captains of smaller vessels or First Mates of larger ones.
This is backed up by the fact that the Pirate society consisted of many men seeking freedom from Colonialism or the slave trade. There has also been evidence that some of Edward Thatch's (Blackbeard) crew were of different races, but were treated just as well as any other crew member.

I believe David's answer covers the rest, but for reference, I suggest the book "The Republic of Pirates" by Colin Woodard. It gives some excellent information on Pirate lives.

Cheers!

I'm drawing on The Many-Headed Hyrdra by Peter Linebaugh and Marcus Rediker. While most of their evidence on black pirates is from the early decades of the 18th century, they do include some late 17th century material.

Yes, black pirates (both free and escaped slaves) formed parts of multinational crews in the Caribbean and off the east coast of America. Linebaugh and Rediker suggest there were likely hundreds of black pirates between the 1690s and 1720s, present on virtually every ship (including those of the famous eighteenth-century pirates Samuel Bellamy and Edward Teach aka Blackbeard). Racial barriers mattered little, and some blacks held trusted roles on pirate ships. Linebaugh and Rediker argue, "The pirate ship was democratic in an undemocratic age...The pirate ship was egalitarian in a hierarchical age." (p. 162-3)

The book also mentions Native American pirates (p. 165), but the reference is from 1717.