How can I deal with my parents, who are angry about my travel and marriage for the sake of da'wah and study? And is not responding to their aggressive messages considered an act of righteousness or disobedience? What is the correct way to treat them in a manner that does not displease Allah?

The pleasure of one's parents is among the greatest acts of worship and a source of good in this world and the Hereafter. Therefore, you must strive to earn their pleasure, treat them kindly, and seek help from Allah, and then from righteous people. If a direct response increases their anger, then it is an act of righteousness not to respond directly. However, avoid not responding at all so as not to provoke them, and it is possible to respond in an indirect manner with politeness.