If you’re reading this, the world did not end. No galaxies collapsed. No universes imploded. All is as it was – and, possibly, even a little better.

Which is to say that, on Sunday night on BBC One, the 13th Doctor – and first female in the role – made her full-episode debut and everyone survived.

Peter Capaldi had reincarnated as Jodie Whittaker – arguably best known for her role as the grieving mother Beth Latimer in Broadchurch, new Doctor Who showrunner Chris Chibnall’s ratings-smashing ITV drama – in last year’s Christmas special amid a welter of controversy.

How, argued some, mostly on red pill Reddit and other ragey parts of social media, could you have a Time Lord sans penis? Others replied spiritedly that you can have a Time Lord with an extra heart, the gift of immortality and the ability to break every law of physics under this or any other sun. You just suspend your disbelief and … make it so.

But – to quote from a recent comment from what we will call the Enraged Community that I came across – it would turn Doctor Who into “joyless, resentful, bitter, intersectionalist, feminist/LGBT propaganda!” “No,” replied the unenraged cheerily, “it won’t! At most, it’ll redress the representational balance in the cultural universe an infinitesimal fraction, but there’ll be no real disturbance in the force” – before realising that their references had strayed into the wrong sci-fiverse and beating a hasty retreat.

TV history was made when Whittaker became the first woman to play the title role since Doctor Who began 55 years ago. Photograph: Sophie Mutevelian/PA

There were also pockets of quiet sadness at what amounts for long-time fans to a breaking of some kind of link with childhood. There was also some grief among those for whom the Doctor was the only pacifist, brains-over-brawn role model they had to show their sons. But overall there was jubilation or at least recognition that the time had surely come. Plus, as the Doctor says in the first episode as one of her new team struggles to process the spooky happenings: “All of this is new to you and new can be scary. Don’t be scared. I understand.”

Whittaker was great and will surely become even more so as the series goes on. At the moment she is a (deliberately calculated, I mean, not accidentally imitative) mixture of Capaldi and something new, as the doctor has not yet fully completed regeneration when the latest dastardly alien plot unfolds. She arrives on Earth without (ahem) a sonic screwdriver, but this lack of vital appendage is – and let this be the show’s wordless lesson to Redditors all – rectified by the end of the first half of this two-parter.

Strict warnings about story spoilers have been issued – and who would want to ruin it anyway? – so let’s just say it involves a missing girl, an interplanetary hunt, daffodil-bulb-shaped travelling pods, a ball of writhing tentacles, glowing collarbones and a daring rescue, all set in Sheffield and all bound together by a sense of shared love, fun and joy.

And it’s this, not the Doctor’s chromosomal arrangement, that is actually the most crucial difference between this series and its immediate predecessors. By the end of the last series – after eight years under Steven Moffat’s aegis – the show had become so narratively bloated and intricately self-involved that any newcomers were in effect shut out. Viewing figures more or less halved from re-inventor Russell T Davies’ showrunning peak.

Jodie Whittaker as Doctor Who. Photograph: Ben Blackall/PA

Last night’s opener from Chibnall was different. It had a webby but comprehensible plot, working on a human scale and with recognisable emotions conducted at a reasonable volume (I know I’m 108 years old, but why have all recent doctors – save the extraordinary and underexploited Matt Smith – been so SHOUTY?) and it was accessible to all.

The new Doctor and her team – 19-year-old Ryan, his old schoolmate turned police probationer Yasmin, and Ryan’s step-grandfather Graham (Tosin Cole, Mandip Gill and Bradley Walsh respectively) – have heart and soul, and are set against a comforting background of South Yorkshire women – especially Ryan’s nan – talking common sense as alien life and electrical pulses erupt around them. Think of it as Happy Uncanny Valley. I hope intersectionalist feminist propaganda is always this much fun.