You've got it backwards. All non-anonymous accusations should be taken seriously. The problem in the story described by this article was the weight being given to anonymous accusations, which should not be given much weight. As a general rule, justice is well served so long as the accused have certain rights, in particular:

"In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial, by an impartial jury of the state and district wherein the crime shall have been committed, which district shall have been previously ascertained by law, and to be informed of the nature and cause of the accusation; to be confronted with the witnesses against him; to have compulsory process for obtaining witnesses in his favor, and to have the assistance of counsel for his defense."

Anonymous accusations have not played a very large role in the more dramatic cases we've seen over the last two years.

Amber Anderson is a real person. Kate Beckinsale is a real person. Angelina Jolie is a real person. All of them made public accusations against Harvey Weinstein.

E. Jean Carroll is a well-known journalist who accuses President Trump of raping her.

Andrea Constand is a real person. Her accusations against Bill Cosby were not anonymous.

Most of these people are well-known, and are putting their reputations on the line by accusing Weinstein, Trump, and Cosby. Such accusations need to be carefully investigated. In the past, these accusations have not been taken seriously and a new seriousness on these matters is overdue.