That people can say this and believe it is one reason there’s still race problems in the world.
The only answer to this is the same answer we have for any point of etiquette: People expect that others expect certain things, so they will be negatively shocked when those expectations are not met in order to keep up appearances around those others who may or may not even exist. The nonexistence of those others, the people who are legitimately shocked by perceived violations of the rules of etiquette, is largely irrelevant; those people mostly aren’t the ones in power, but the ones who are in power will punish you on their behalf often enough that serious breaches of etiquette are rarely worth it, and kids don’t know how to pick their battles.
As a more pointed example: The police don’t give a shit if you walk down Main Street naked. They have a thousand other things to do that day and someone getting a mild sunburn rates below minor traffic infractions on the list of things other people do which can harm the innocent. However, the police will likely arrest you for walking down Main Street naked, because of laws passed by politicians who didn’t, themselves, care about public nudity but wished to protect children from human anatomy. It’s a whole chain of pass-the-buck outrage-by-proxy which results in naked people going to the county jail. It isn’t a conspiracy, it’s just people acting as they think other people expect them to.
The N word and the F word aren’t even in the same realm as each other, in my opinion. One is used to deliberately denigrate a group of people; the other is a far more casual way of saying sex.
To the OP, I do curse around my 13 and 10 year old, but sparingly, and usually only then if I’m really ticked off and never, ever at them. I don’t see anything wrong with cursing as a way of expressing frustration (and it has the added side effect of really grabbing my kids’ attention when I do it because they almost never hear it from me). That said, cursing is usually used to express added disgust or a particular disregard for someone or something. If you’re trying to teach kids to be respectful or kind, adding that extra dose of crude emphasis isn’t a good way to do that.
…And I thought that there were four categories I was trying to remember, not just three. There are curses, profanities, obscenities, and swears. Swears are usually profanities, and curses often are, but either of them can be non-profane.
For me it really is about setting an example of appropriate speech, not shielding them from hearing the words (which is a task that I consider impossible).
So I try not to curse in front of my children. But I don’t lose any sleep when I slip up. And we set very clear expectations about what is appropriate (for them, the words are never appropriate).
I also don’t go to great lengths to shield them from hearing the words. I listen to my indie-rock/alternative music in the car (which they like and often know the lyrics to). But they know not to sing the bits that have the bad words even though I haven’t explicitly asked them not to.