It is both socially unacceptable and a criminal offence to make critical or defamatory remarks about the royal family.
Thailand's monarchy might be a constitutional one, but almost every household displays a picture of King Bhumibol and Queen Sirikit in a prominent position, and respectful crowds mass whenever either of them made a public appearance. The second of their four children, Crown Prince Vajiralongkorn was Crowned as Rama X in May 2019; his younger sister, Princess Royal Maha Chakri Sirindhorn, is often on TV and in the English newspapers as she is involved in many charitable projects. When addressing or speaking about royalty, Thais use a special language full of deference, called rajasap (literally "royal language").
Aside from keeping any anti-monarchy sentiments to yourself, you should be prepared to stand (although less observed these days) when the King's Anthem is played at the beginning of every cinema programme and to stop in your tracks if the town you're in plays the national anthem over its public address system – many small towns do this twice a day at 8am and again at 6pm, as do some train stations and airports. In the past it's been quite a regular occurrence for us. A less obvious point: as the king's head features on all Thai currency, you should never step on a coin or banknote.