His parent ordering him to do something that people consider shameful

A: If what they asked you to do entails disobeying Allah, it will not be permissible to obey them; rather, you should point out to them kindly that it is disobedience to Allah and therefore should not be done. You should do what pleases them as long as it is not a sin. However, if you think that what they ask you to do is a shame such as making an announcement about something lost, etc, then obeying them is Wajib (obligatory) and you should carry out what they ask you to do or deputize someone else to do it for them or nicely apologize to them until they are satisfied. Allah (Exalted be He) says, And your Lord has decreed that you worship none but Him. And that you be dutiful to your parents. If one of them or both of them attain old age in your life, say not to them a word of disrespect, nor shout at them but address them in terms of honour. And lower unto them the wing of submission and humility through mercy, and say: "My Lord! Bestow on them Your Mercy as they did bring me up when I was young." (Part No. 25; Page No. 227) May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.