As I see it, you have 4 options: Move out. Have a big fight over cursing. Try to negotiate some meeting in the middle. Or learn to ignore it.
Moving out will remove you from the situation but it’s likely to still go on whenever you visit. If having long breaks from it is all you are looking for, that might be a good option. Fighting about it or being confrontational isn’t likely to work. You can’t make other people do or stop doing anything. If you argue about it, they may just stubbornly tell you they have a right to talk the way they want to. It could even get worse!
You might be able to negotiate a little less swearing in the house if you can appeal to their better selves and tell them how uncomfortable it makes you. If you can do this without sounding like you feel superior to them, they might listen. Emphasize your discomfort, not that you think they are “wrong” to do it and you’ll have a better shot at a real conversation.
It could also be that one of the reasons your brothers do it is because you react so strongly to it. If that’s the case, it’s an immature but fun game for them. The best thing to do then is to learn to ignore it. If you don’t react, they won’t get the payoff they are looking for. You do have the option of becoming “curse deaf” you know, and just letting it roll off you.
At 23, you are old enough to analyze the situation and to consider what your goals are. If raising the issue will separate you from your family, is it really worth it? You do have choices.
I wish you well.