The paper by Gil Sharon and colleagues  has certainly created headlines and discussion in equal measure (see here and see here and see here and see here). Concluding that: "Mice harboring human ASD [autism spectrum disorder], but not TD [typically developing], microbiomes exhibit ASD-like behaviors", the idea of a gut-brain connection in relation to autism (see here) potentially gains some research traction.
The Sharon study involved transplanting gut bacteria - the gut microbiome - from a small number of participants - "from 5 control volunteers and 11 patients diagnosed with autism spectrum disorder" - into mice lacking a microbiome and breeding said mice. They then analysed the behaviour and other biological parameters of those offspring mice according to whether their mother mice had received a transplant from controls or participants with various 'degrees' of autism. They also looked at 'metabolite profiles' based on "analyses of colon contents from oTD [offspring typically developing] and oASD [offspring autism spectrum disorder] mice."
Results: "colonization with ASD microbiota is sufficient to induce hallmark autistic behaviors." By 'hallmark autistic behaviors' researchers observed that said mice showed "increased repetitive behavior, decreased locomotion, and decreased communication... compared to mice colonized with samples from TD controls (oTD), as tested by marble burying (MB), open-field testing (OFT), and ultrasonic vocalization (USV), respectively." Researchers also observed specific differences across the mouse group gut microbiomes, some of which were consistent with that noted in other independent studies.
Also: "Twenty-seven out of 313 detected metabolites were significantly different in the colon contents of oASD mice, compared to oTD mice." They specifically focused in on two metabolites - taurine and 5-aminovaleric acid (5-AV) - both of which were reported in lower levels in the oASD mice, and how these compounds show a *connection* to GABA, a compound potentially important to autism (see here). Further they showed that supplementation of 5-AV and taurine to another strain of mouse that serves as a 'mouse model of autism' (BTBR T+ tf/J (BTBR) mouse model) resulted in "improved repetitive and social behaviors." I should add the word 'mouse' into the sentence "improved repetitive and social behaviors."
Insofar as the limitations of the Sharon studies and paper, various people have been keen to point out that the results should be viewed cautiously and as preliminary. This on the basis of the number of animals included for study, the reliance on mouse models of autism (and the logical fallacies that can sometimes follow) and some of the generalisations made in the study write-up by the authors. I wouldn't disagree with such cautions, bearing in mind that some mouse models of autism - the valproic acid autism mouse model for example - actually seem to be pretty good at mimicking some facets of (induced) autism. I'd also point out that the metabolomics work undertaken by Sharon and colleagues looks to be pretty wide-ranging (GC-MS and NMR are discussed) and findings related to taurine have also been noted in other independent study (see here). I also observed that there was a research tie-up with Arizona State University in the Sharon study, as the name Dae-Wook Kang is mentioned and 'poo transplants for [some] autism' makes yet another appearance (see here and see here).
"While ours is a limited study, with 16 donor samples from a pediatric cohort, the results support a hypothesis that the human gut microbiota contributes to ASD phenotypes." I'd agree that the Sharon results add a further layer to the idea that the new triad - intestinal permeability, mucosal immunology and intestinal microbiota - could be important to at least some autism. The results offer a road map for further investigation in this area and perhaps eventually, yet another avenue for screening and intervention to complement other recent initiatives (see here); all set with the view of the (plural) 'autisms'.
Finally, I note that another study  mentioning the words 'mouse' and 'autism' has been published recently. With some media attention mentioning how: "Exercise reversed autistic behaviors in an animal model of the condition" there didn't seem to be the same 'keenness' to point out the flaws of the Andoh study, despite once again a reliance on 'mouse autism' and all which that entails. It makes me wonder whether the focus on the second brain (gut) and autism detailed in the Sharon study might still have the ability to raise hackles in some quarters?
 Sharon G. et al. Human Gut Microbiota from Autism Spectrum Disorder Promote Behavioral Symptoms in Mice. Cell. 2019 May 30;177(6):1600-1618.e17.
 Andoh M. et al. Exercise Reverses Behavioral and Synaptic Abnormalities after Maternal Inflammation. Cell Reports. 2019; 27: 10. June 4.