This seems to be a trend with toxo papers - take a too-small sample, do no power or Bayesian analysis, find all bad correlations, but declare evidence of safety anyway.
The abstract as written is simply wrong from a statistical point of view:
our study strongly indicates that cat ownership in pregnancy or early childhood does not confer an increased risk of later adolescent PEs [2]
If you instead adopt Bayesian reasoning, then the direction of the measured effect is weak evidence that cats cause illness later in life. Either way you cut it, the study author's interpretation fails to coincide with the actual data they collected.
[1] https://liesandstats.wordpress.com/2008/09/08/accept-the-nul...
[2] https://www.cambridge.org/core/journals/psychological-medici...
Edit: Source: Neuroscientist, multi-term dean, honorary doctor, and I would keep going but it would end up personally identifiable. Let's just say I have this on extremely good authority. There's a reason why "Most science research findings are false. " https://qz.com/530064/most-science-research-findings-are-fal...
Only the 0,7% on average of the cats drop oocysts in its faeces and it still will take 1 to 5 days for this oocysts to activate and be able to transmite the disease. If you clean daily the litter box of your cat with gloves and you are not pregnant or inmunocompromised the problem is greatly minimized.
I would speculate that having a dog would be a better after the fact indicator of mental illness considering their more frequent use in animal assisted therapy.
Only to those possessed by cats.
Q.E.D.
