Is it finished yet? Also, #MustelidRights.

After many rewrites and new versions, yes! The final version was published in 2019, along with a sequel - more is to come later this year. https://www.amazon.com/dp/B00X3NC5MC

Also, a bit of perspective from a Catholic: If the Vatican became aware of the mustelids' condition of soul; that, for all intents and purposes, they are humans with a stoat skin, they would more than likely change their position on them as it is unlikely that it had been made a matter of dogma. In fact, the Vatican would more than likely end up championing for mustelid rights.

Also, I wonder if the reason why they don't allow leather on the teleporters is that it can fry them. Don't mustelids such as stoats have leathery skin?

Unfortunately, the Vatican do not consider the starats (the updated name for mustelids in later versions) as humans in a furred skin. Due to some plot reasons that are explored later on, they are considered a blasphemy and a corruption of the pure human form.

[T]hey are considered a blasphemy and a corruption of the pure human form. I understand "Made in God's Image and Likeness," but the soul is what matters on Judgement Day, is it not? If not, then how would you consider those who use silicone enhancements or botox? If my understanding is not within Catholic teaching, correct me, but I find the soul matters, not the shape. After all, how would extraterrestrials attain salvation? Surely they would also have a place at Heaven's banquet.

(Going to be sharing this on r/Catholicism to see where my understanding lies in relation to church teaching.)

I think it's important to distinguish that this was never intended to be a 1:1 facsimile of the Catholic church as it is in our time. In the intervening 600 years or so before this story is set, there has been a lot to change within the organisation. Due to plot events that take place later on in the series, it is clear that this version of the church is a corruption from its modern self.

"And the gates of Hades shall not prevail against it."