The subjects that most reliably need care worldwide: domestic politics, religion, historical grievances, and money, with each country adding its own specific tripwires, usually involving borders, wars, colonial history, or neighbouring states. These are the topics where a visitor's casual opinion can land as an insult, so the working rule is to ask rather than assert, and to let locals criticise their own country without joining in, a restraint that is appreciated everywhere. In a few countries, disrespecting the monarchy or founding figures is a legal matter, not just a social one, which official travel advisories will flag.
Money and personal life split by culture: questions about salary, rent, marriage, and children are ordinary friendliness across much of Asia, Africa, and the Middle East, so expect to receive them and deflect lightly if you prefer; raising the same topics unprompted in Northern Europe or North America can seem intrusive or boastful. Comments on weight, age, and appearance are casually made in some cultures and offensive in others, so give none until you know the terrain.
When conversation drifts somewhere delicate, the graceful exits are curiosity and redirection: ask a question about food, travel, family pride, or local sport, all near-universally welcome. And if you misstep, a light apology and change of subject repairs it; laboured backpedalling only extends the discomfort.