LONDON — When Olly Alexander burst into tears shooting a scene of “It’s a Sin,” no one was very surprised. Making the show, which came to HBO Max on Thursday and follows a group of friends embracing the gay culture of ’80s London under the shadow of AIDS, was emotional for many of the cast and crew — and Alexander is as comfortable showing his vulnerabilities as the character he plays, Ritchie, is at deflecting them. “I was a complete mess after the first take,” Alexander, 30, said in a recent video interview. “I was sobbing.” Peter Hoar, the director of “It’s a Sin,” paused filming.