The word ticklish means both "sensitive to being tickled" and "requiring tact or careful handling." A lot of people avoid ticklish subjects when they meet someone new, instead sticking to safe topics like the weather.
You know you're ticklish if you squirm and giggle when your friend tickles your feet. You're also ticklish if you're easily upset or irritated. For you, ticklish subjects might include politics, conspiracy theories, and which musician should have won a Grammy. That means those topics are particularly difficult, requiring a careful, tactful person to keep you from getting upset about them. This figurative sense predates the literal one, and an earlier version was tickly.