One afternoon last month, Chad Nedohin, a part-time pastor and die-hard supporter of Donald J. Trump, put on a pirate costume, set up his microphone and recited a prayer.

Mr. Nedohin was opening his latest livestream on the right-wing video site Rumble, where he has about 1,400 followers who share a devotion to Trump Media & Technology Group, the former president’s social media company.