The company has required notarization for apps (which gives them a Developer ID) since macOS Mojave 10.14.5, but warnings will soon become error messages for Catalina users. Apple had originally intended to clamp down when Catalina was available, but decided on a transition period to help developers adapt.
As you might imagine, this is all part of a push for greater security. The notarization not only prevents people from ‘casually’ running malware, but lets Apple take action if there’s a major security flaw or another serious problem. You’ll have to understand the risks if you want to run software without those safeguards.