Of course Hasbro wanted Beast Wars to distance itself from G1/G2. This is because Transformers was incredibly poor by 1995. They wanted Beast Wars to revitalise the franchise, but they were afraid that too close an affiliation with the failing Transformers brand might drag Beast Wars down. This is why the "Transformers" logo is so small on early Beast Wars packaging and is placed beneath the "Beast Wars" logo. Hasbro saw Transformers as a sinking ship, and Kenner wanted to see if they could revive it without being dragged down by the failing G2 line.

Remember that very early Beast Wars continuity was a direct sequel to G2. I'm talking about the toy canon that existed before the cartoon came out. According to this, the Maximals and Predacons were the Autobots and Decepticons rebuilt thanks to bioengineering. But it was Mainframe who wanted to shake off the shackles of G1/G2 and decided to further separate the Beast Wars cartoon. They made the decision to make the Maximals and Decepticons the descendants of the Autobots and Decepticons and to start these characters from the far future. In the very first episode we soon learn that the Cybertronians have been at peace for a long time, but that the peace wasn't as enjoyable for the underprivileged Predacons.

As time went along, yeah, the show became more closely tied with G1, but this started in Season 1. We had things like Starscream's Ghost appearing, references to Unicron and the establishment that the Maximals and Predacons were indeed descendants of the Autobots and Decepticons, who they regard as being part of their ancient history. Yes, the writers did keep in close consultation with the online fanbase and they did take a lot of advice from fans. But I think that's a strength of the show because it allowed them to better give fans what they wanted! And remember that Larry DiTillio is notorious for being a world builder. He's kinda like Tolkien in a way that he sits down and fleshes out the fictitious world that his characters inhabit. Bob Forward not so much, but DiTillio was very much a world-builder. It was even DiTillio's idea to tie Beast Wars in with G2 continuity, such as establishing the Vok as being an evolution of the Swarm etc.

And this fan relationship was important because remember that Bob Forward and Larry DiTillio knew practically NOTHING about Transformers before they started writing Beast Wars. They used their own personal spare time communicating with fans online and getting the fans to educate them about Transformers. It was the fans that provided them with information. Tfwiki didn't exist back then, they couldn't just Google^Yahoo! it. And no, their research wasn't always perfect... but at least they made the effort! Compare this with Michael Bay! Beast Wars isn't perfect, but at least the writers gave a crap about the Transformers. They wanted to tell a good story. They actually cared about what fans thought and took advice from the fans - they listened. And the BW show is chock full of references to the fandom because of the interaction between the writers and the fans! Starbase Rugby, Sub-Sector Hooks, Wonko the Sane etc. In fact, the writers even wanted Peter Cullen to make a cameo appearance as Optimus Prime, but Cullen refused due to industrial issues between American and Canadian voice actors at the time (despite Cullen being natively Canadian, but he wanted to support the American voice acting industry). They also wanted to play part of the G1 theme music but were unable to secure the rights from Sunbow. There were actually more G1 connections that the writers wanted to put into the show but were unable to. DiTillio and Forward took it upon themselves to learn about the Transformers and tried to write good Transformers stories. Michael Bay initially hung up on Steven Spielberg when he was first pitched the idea of directing a Transformers movie - he was then given a grand tour and "schooled" about Transformers by Hasbro... and despite all that support that Hasbro gave Bay which they never gave to Forward and DiTillio, Beast Wars still worked out to be a far better story than Bayformers. Beast Wars enhances and enriches G1. Bayformers kills your childhood.

Beast Wars is absolutely a sequel to the G1 Continuity Family and not directly to the G1 cartoon continuity. You could try to fansplain it like some bad fanfic, but ultimately any fansplanation would be non-canonical anyway. Beast Machines has stronger ties with the G1 cartoon, but that's not surprising considering that G1 cartoon writer Marv Wolfman wrote more episodes for BM. He did co-write one episode for Beast Wars which was "The Probe." This was the episode that made me sit-up and really take Beast Wars more seriously, as it was the first Transformers episode that I'd ever seen where the bad guys won a decisive victory! When the credits for that episode rolled, I sat back thinking, "Wait... did the good guys just LOSE?!?" It was then that I realised that the gloves were off.