Remember that Beast Wars never followed on from any one G1 continuity, but rather fits into the overall G1 continuity-family. This is really because Larry DiTillio and Bob Forward knew almost nothing about Transformers when they were employed to write the show and they went and looked at various different sources and implemented them into the world of Beast Wars. Some elements of BW draws from the G1 cartoon (e.g. Starscream's ghost and how he became a ghost), the Marvel comics (e.g. Covenant of Primus, the intended and now retconned connection between the Vok and the Swarm etc.), the tech specs (e.g. Ravage's appearance and portrayal in BW was based on his G1 tech specs profile) etc etc.
Vector Sigma (G1 cartoon) also exists in BW and BM, but in BW it behaves like Primus (even to the point that Unicron perceives it as a divine rival); yet in BM we see that they still have the Key to Vector Sigma, which apparently is a program and not just a physical key (as the original key was destroyed by Silverbolt). We see images of the Golden Age and the Hate Plague which also comes from the G1 cartoon, but yet Cybertron still has a moon which contradicts the G1 cartoon.
Cos he's that awesome.
That's how Beast Wars was written - see comments above. It's best to think of Beast Wars as fitting into the G1 continuity family rather than into any single continuity.
That wasn't Mainframe's fault ... blame Kaneda Masumi/Toei. But then again, it was an understandable mistake. Remember that Transformers The Movie didn't come out in Japan until much later, so at the time they wrote The Headmasters TFTM wasn't available to the Japanese market... so it's understandable that they didn't realise that Prowl had been killed in TFTM and thus inserted him into the Headmasters. Now of course, since TFTM came out in the JP market it's created a continuity headache which Binaltech has since retconned with the character of Prowl II.