Honestly (and I see you do recognise this in your comment) but this really seems like a kinda crappy study that I'm surprised made it into plos.
For instance I couldn't find any evidence of them considering that the dietary choices of the guardian may affect the attitudes of the guardian to vetenarians (and thus the self-reported health of those animals). To take this further, in the scenario that a cat guardian believes their choices make their cat healthier, especially when going against vetinary orthodoxy, the guardian is probably less likely to take the cat to the vet for minor issues. This confounds the analysis of "healthiness" as performed by the authors.
Furthermore any cat that is not an indoor cat is likely also not fed a purely vegan diet (as they do hunt), so they should possibly account for that via a sort of bootstrapped approach. Generally the stats were okay though, and don't make super strong claims from some pretty weak data. Though GAMs were a pretty odd choice and I'd have preferred some sort of explicit model fit with Bayesian fitting or NLLS.
In the end all of this points to the sort of thing where they should really have been doing perturbational research. I.e. feeding cats different diets in a controlled lab space. This is not the sort of research that lends itself to surveys and that seriously impacts the actual practicality of its findings.
Also as an aside, I really cannot abide anyone who includes a questionably inspirational quote that they said themselves in the fucking French Alps on their own website. That's just pure wankery. The only people I usually see doing things like that are scientists like Trivers, which is not company one should wish to be in.
I'm sorry, I'm confused here. I'm obviously all against race science and greenwashing, but I was talking about the quoted study in my post.
That aside, it definitely is good to have more people talking about the inherent subjectivity and impermanence of science though!