Dungeons & Dragons is a game that is best played in a group of adults. Yes, kids can play it but the game really comes into its own when grown ups are driving the party. That said, here are some items specifically pointed to the adult players.
Nowhere is it written that part of the Dungeon Master's obligation is to manage your ability to get along with the other players. It's assumed you can handle that on your own. Now, it's true that sometimes two people just can't get along, even if they're making a genuine effort. If that's the case, then it may not be a terrible idea to ask the DM to sit down with the both of you to talk it out. The DM is the choice here because sometimes members of a group don't know each other as well as they know the DM, so having a mutual friend present can help. Keep in mind that this situation is putting the DM into a bad position. You may very well be creating a situation that forces the DM to choose between you and another friend. That isn't fair, and it puts at least one friendship in jeopardy. If that DM has to choose between you, somebody's getting hurt.
In every D&D group there's at least one player who has the free time, the energy or the amazing memory to all but memorize the entire contents of the Player's Handbook. In and of itself, that's not a bad thing at all. Having a living rules wiki sitting at the table can save a lot of time. There can be a downside though.
If you're that player, and you know the rules so well that you find yourself constantly correcting people, stop. On big, important things, by all means mention it and help people to learn the rules better. What you do NOT want to do is nitpick. People generally don't mind being corrected from time to time, but if they feel like you're policing them, they'll start to resent it. D&D is a complex game, filled with plenty of special, unique cases where the rules interact in a complex way, or sometimes don't cover the situation. Let the DM handle it. Sometimes a DM has to bend or even break the rules in order to handle a particular situation in a fair and equitable manner. The DM is empowered to do this.
Some people LOVE to talk about their views. They eagerly await any opportunity to share their perspectives and beliefs, and will readily engage in a discussion about them. Some of those people are actually able to be reasonable even with those with whom they disagree.
If that's you, great. But if you're the sort of person who becomes emotional during a political debate, or if you find it insulting when people don't share your views and concerns, then you're better off keeping your mouth shut. This isn't to protect others from you, it's to protect you from yourself. Don't ruin everybody else's good time just because you switch out of adult mode whenever someone says to you: "I disagree." You will soon find yourself out of a D&D group.
Keep your bigotry to yourself. There are plenty of people out there who have an axe to grind against some group or another. Probably more people than you might think. (Personally, I can't stand Penguins fans.) Some hate black people. Some hate white people. Some hate Muslims. Some hate Christians. Some hate women. Some hate men. Some hate Pittsburg Penguins fans (which is entirely understandable, TBH) while other delusional people hate Washington Capitals fans. Whatever your particular problem is, don't assume the others at the table share it. Don't assume nobody at the table is a member of the group you don't like.