Board gamers tend to be a bit less toxic than players of some of the other gaming cultures, such as video games, roleplaying games, and collectible card games. These latter cultures notoriously attract vocal racists, sexists, homophobes, etc etc. "Gamergate" is all I have to say about that. Board gamers tend to be more gender-mixed, more family-friendly, and older (but not as old as miniature war-gamers and the like).
Unfortunately, like every subculture, the board game culture is set within the real world, and so there is plenty of racism, sexism etc in it (it's just not generally a seething wretchedness, like it is in video games or certain sports). The more fanatic the gamers, the more racist, etc they tend to be. Fanatics don't want anything messing with their hobby, especially when the messers point out problems with their privilege. In my casual estimation, there is a tendency toward racism among certain hardcore game fanatics on BoardGameGeek, and probably other, similar websites.
As for the game designers and publishers, there are plenty of tone-deaf tabletop games (and of course video games), steeped in white privilege. Last year, for example, a board game called Scramble for Africa was canceled after complaints that it presented the colonization and pillage of Africa as a means of obtaining points. It even used events, such as causing local "uprisings", as a game mechanic to further your position, without addressing the native population and the effects that the colonization had on the continent. Similar complaints have been leveled at any conquest game, including such abstracts as Catan; not because Catan represents a particular oppression, but because the very act of conquering and transforming a supposedly uninhabited territory is a kind of whitewashing.
Plenty of other games have whitewashing problems, such as the well-loved Puerto Rico (with brown "colonists" working in the plantations of San Juan) and Endeavor (where slavery cards are a cheap tool for points, and freeing the slaves is another one).
As I mentioned, collectible card games attracts some real bigots, probably because the same population that plays it tend to play video games. As a result, there is a dearth of black Magic players. Wizards of the Coast was taken to task, not only for not doing enough to address the racism of its conventions and game groups, but for its unsafe work environment and even the artwork on its cards. After Zalem Beg, a former editor-in-chief for major Magic: The Gathering retailer and several other top sites, recently wrote a scathing attack on the company's culture as well as some of its cards and web site choices, yesterday Wizards finally responded by banning some old cards and racist artwork.
I know that TSR and then Wizards of the Coast also had a history of racist portrayals and/or exclusion of minorities in their Dungeons and Dragons products, and I know that they have included more minorities, with less stereotypes, in some artwork in recent years, but they still have a ways to go. Some people object to the very idea of D&D as a cultural appropriation and glorification of killing the "other", and others to how orcs seem to represent the other in a racist way (a problem that they say originated from Tolkein).
In April, world Chess champion Magnus Carlsen marked a U.N. international campaign against racism by playing a game of Chess where the black pieces moved first. In Chess, both sides play with the exact same pieces, just different colors (sometimes not even black and white), and every other classic abstract game, including Checkers and Go, has the black pieces moving first. Meanwhile, the Chess world, like every other world of fanatic hobbyists, is pretty white, for the various reasons you might expect, including lack of, or thwarted, opportunities and microaggressions in Chess groups and culture.
Same goes for other games with single-minded devotees, such as Scrabble. Speaking of Scrabble, years ago some people objected to racist terms being in the Scrabble dictionary (it took years before these terms were even labeled as offensive in the dictionary); they were removed, but remain valid for tournament play on a special sheet handed out to tournament players, and you can still play them online if you select the tournament dictionary.
Tom Vasel recently interviewed designer Eric Lang to get his take on being black in the board game community. Eric Lang is a notable and successful game designer, unfortunately one of the few who are black.
The Game Manufacturers Association who run the Origins convention was taken to task for NOT saying anything about black lives matter. As a result, Eric Lang and many other invited speakers pulled out of the convention. Yesterday, GAMA finally put out a statement about black lives matter and canceled the event. People continue to take them to task for canceling the event as if it had been their decision, and not the result of their previous lack of statement.
And of course, on the flip side, people can create tabletop games that teach about racism and how we can deal with it. Not that many, exist, however.