But are they credible? Someone could (and probably has) write a bot to make idle threats against dozens of feminists on a daily basis. Should the police investigate every one of them?

The key here is that they're not threatening to commit a crime - the threat itself is the crime.

If a man on the internet says that he's gonna come to your house tonight and rape you, and then it turns out that he lives in Britain and you live in Canada, does that make getting the rape threat any less terrifying?