If they wanted to do a gender-swapped Doctor Who, without it being the absolute pile of dogshit that is the BBC's current attempt, they should cast Fern Brady

Current attempt? That series ended two seasons ago. The current doctor is Ncuti Gatwa, and we even had a brief spell of David Tennant again in between.

My phrasing was bad. Both the gender-swapped and the current "dancing in the crosswalk" Doctor Who attempts were dogshit. Fern Brady would actually fit the emotional timbre of the classic Doctors while also happening to be modern and female, was my point.
- What's wrong with Ncuti?

Current attempt? You mean the attempt from 5 years ago or the one that isn't happening for another year?

Wait, they're getting rid of Ncuti? Nooo,,,,,
- Yes, because of Disney's refusal to commit to the series. The production schedule is entirely too unpredictable right now, and Ncuti has (a lot of) other offers.
  I can't elaborate without major spoilers.
- after getting rid of jodie from the previous series.

I'm not a doctor who fan at all, so as far as I'm concerned the show is dogshit regardless of who the doctor is, but that's my personal taste, to each their own.

However, from a couple minutes of googling, I'm pretty sure that the most recent doctor was a dude, and the next season with a new ("gender swapped") doctor hasn't even aired, or even been given an official release date, so not sure how you can really judge it already. Maybe you don't like the actress, but I know I've been surprised by actors I generally don't like knocking it out of the park before.

There was another female doctor prior to this most recent one, but again, you've had a whole 'nother doctor since then.

So I'm really not too sure what you're on about their "current attempt."

Maybe you don't like the actress
No idea about her or anything upcoming. I thought it was universally accepted that the recent seasons of the Doctor were horrible, but it looks like I'm alone in that. Oh well. Anyway, my main point about this was that Fern Brady would do great.

As much as I love Fern Brady, she’s not an actress! Although a double-Doctor 70th anniversary with her and Capaldi could be entertaining.

I’ve not once thought gender was ever an issue for the show. Having seen Jodie Whittaker in other things prior to Doctor Who, I was really looking forward to her taking over. Same for Ncuti, and I think they both did well given what they had to work with.

I don’t think the writing was even that bad, except for the odd terrible episode, but all seasons had duffers. Changing too much too soon has affected it badly. It’s strayed too far from the previous family friendly show, possibly thanks to Disney and the need to explain it all to a new audience.

We need a new Matt Smith-esque era.

She did do acting before she did comedy, probably nothing anyone's ever seen.
It looks like I'm not alone in having the impression that the most recent seasons were badly received: https://www.imdb.com/title/tt0436992/ratings/
I don't think it was that gender "was an issue" or anything. Like I say I thought it was just kind of generally understood that the recent seasons just weren't very good, but it looks from the comments like that's not the Lemmy consensus, so be it.
The biggest problem I had with the Jodie era was the companions.
Doctor Who has a rich history of the Doctor/Companion interactions following traditional gender roles. The Doctor is a powerful man who can bend time and space to his will, and his companion is an empathetic woman who can keep him grounded and retain his humanity. While there have been exceptions, this is the default formula.
When Jodie started, this all got turned upside-down. How should a woman Doctor act? Do they maintain the same character archetype (as they did with the Master/Missy), or do they make the character more feminine? What effect should that have on her relationship with her companions? Should the companion continue to be the traditional feminine role? Headstrong and masculine, but powerless? Wise and sage, like an advisor? This is a difficult plan for even the most accomplished writer.
Chris Chibnall was apparently not up to the task. Instead, he threw all of the options in at once. At best, it felt crowded and disjointed. But more often, it felt like they were focus-group testing. And by the end, it seemed clear that Kaz was the most popular with test audiences.