I answered a similar question (Is autism caused by genetics?) on Psychology & Neuroscience where the following was found, plus I have added information regarding autoimmune responses concerning Autism.
Autism spectrum disorder (ASD) now affects one in 68 births in the United States and is the fastest growing neurodevelopmental disability worldwide (Edmiston, et al. 2017) [free access paper with links to cited papers]. Alarmingly, for the majority of cases, the causes of ASD are largely unknown, but it is becoming increasingly accepted that ASD is no longer defined simply as a behavioral disorder, but rather as a highly complex and heterogeneous biological disorder (Edmiston, et al. 2017).
With the information available, the genetic and environmental causes of Autism is open to speculation and interpretation.
The paper you cited is referenced in Edmiston, et al. (2017) under citation number 28, and they stated (emphasis mine):
there are likely multiple, biologically defined subgroups within the ASD spectrum(3–7). Specifically, there is growing evidence that supports maternal immune dysfunction may underlie the behavioral abnormalities observed in a subset of children affected with the disorder(8). Several immunologic risk factors have been described including: genetic associations with immune-related genes(9–16), family history of autoimmune disease(15, 17–21), maternal inflammation and infection during pregnancy(22–27), and altered immune responses in the children, and are associated with increased impairments in core and associated features of ASD(28). More specific to this review, maternal anti-brain autoantibodies, which are thought to access the fetal compartment during gestation, have been identified as one risk factor for developing ASD and are proposed to contribute to early neurodevelopmental perturbations in the developing fetus(29–31).
- Lord C, Risi S, Lambrecht L, Cook EH, Leventhal BL, DiLavore PC, et al. The autism diagnostic observation schedule-generic: a standard measure of social and communication deficits associated with the spectrum of autism. Journal of autism and developmental disorders. 2000;30:205–223.
- Newschaffer CJ, Croen La, Daniels J, Giarelli E, Grether JK, Levy SE, et al. The epidemiology of autism spectrum disorders. Annual review of public health. 2007;28:235–258.
- Snow AV, Lecavalier L, Houts C. The structure of the Autism Diagnostic Interview-Revised: diagnostic and phenotypic implications. Journal of child psychology and psychiatry, and allied disciplines. 2009;50:734–742.
- Ousley O, Cermak T. Autism spectrum disorder: Defining dimensions and subgroups. Current Developmental Disorders Reports. 2013;1:20–28.
- McDougle CJ, Landino SM, Vahabzadeh A, O’Rourke J, Zurcher NR, Finger BC, et al. Toward an immune-mediated subtype of autism spectrum disorder. Brain Research. 2015;1617:72–92.
- Onore C, Careaga M, Ashwood P. The role of immune dysfunction in the pathophysiology of autism. Brain, Behavior, and Immunity. 2012;26:383–392.
- Warren RP, Singh VK, Cole P, Odell JD, Pingree CB, Warren WL, et al. Increased frequency of the null allele at the complement C4b locus in autism. Clinical & Experimental Immunology. 1991;83:438–440.
- Warren RP, Odell JD, Warren WL, Burger RA, Maciulis A, Daniels WW, et al. Strong association of the third hypervariable region of HLA-DRβ1 with autism. Journal of Neuroimmunology. 1996;67:97–102.
- Torres AR, Sweeten TL, Cutler A, Bedke BJ, Fillmore M, Stubbs EG, et al. The association and linkage of the HLA-A2 class I allele with autism. Human immunology. 2006;67:346–351.
- Campbell DB, Li C, Sutcliffe JS, Persico AM, Levitt P. Genetic evidence implicating multiple genes in the MET receptor tyrosine kinase pathway in autism spectrum disorder. Autism Research. 2008;1:159–168.
- Thanseem I, Nakamura K, Miyachi T, Toyota T, Yamada S, Tsujii M, et al. Further evidence for the role of MET in autism susceptibility. Neuroscience Research. 2010;68:137–141.
- Mostafa GA, Shehab AA. The link of C4B null allele to autism and to a family history of autoimmunity in Egyptian autistic children. Journal of Neuroimmunology. 2010;223:115–119.
- Jung JY, Kohane IS, Wall DP. Identification of autoimmune gene signatures in autism. Translational psychiatry. 2011;1:e63–e63.
- Torres AR, Westover JB, Gibbons C, Johnson RC, Ward DC. Activating killer-cell immunoglobulin-like receptors (KIR) and their cognate HLA ligands are significantly increased in autism. Brain, behavior, and immunity. 2012;26:1122–1127.
- Comi AM, Zimmerman AW, Frye VH, Law PA, Peeden JN. Familial Clustering of Autoimmune Disorders and Evaluation of Medical Risk Factors in Autism. Journal of Child Neurology. 1999;14:388–394.
- Atladóttir HO, Pedersen MG, Thorsen P, Mortensen PB, Deleuran B, Eaton WW, et al. Association of family history of autoimmune diseases and autism spectrum disorders. Pediatrics. 2009;124:687–694.
- Vinet É, Pineau CA, Clarke AE, Scott S, Fombonne É, Joseph L, et al. Increased Risk of Autism Spectrum Disorders in Children Born to Women With Systemic Lupus Erythematosus: Results From a Large Population-Based Cohort. Arthritis & rheumatology (Hoboken, NJ) 2015;67:3201–3208.
- Wu S, Ding Y, Wu F, Li R, Xie G, Hou J, et al. Family history of autoimmune diseases is associated with an increased risk of autism in children: A systematic review and meta-analysis. Neuroscience and biobehavioral reviews. 2015;55:322–332.
- Chen S-W, Zhong X-S, Jiang L-N, Zheng X-Y, Xiong Y-Q, Ma S-J, et al. Maternal autoimmune diseases and the risk of autism spectrum disorders in offspring: A systematic review and meta-analysis. Behavioural brain research. 2016;296:61–69.
- Chess S. Autism in children with congenital rubella. Journal of autism and childhood schizophrenia. 1971;1:33–47.
- Meyer U, Nyffeler M, Engler A, Urwyler A, Schedlowski M, Knuesel I, et al. The time of prenatal immune challenge determines the specificity of inflammation-mediated brain and behavioral pathology. The Journal of neuroscience : the official journal of the Society for Neuroscience. 2006;26:4752–4762.
- Smith SEP, Li J, Garbett K, Mirnics K, Patterson PH. Maternal Immune Activation Alters Fetal Brain Development through Interleukin-6. The Journal of neuroscience : the official journal of the Society for Neuroscience. 2007;27:10695–10702.
- Atladóttir HÓ, Thorsen P, Østergaard L, Schendel DE, Lemcke S, Abdallah M, et al. Maternal Infection Requiring Hospitalization During Pregnancy and Autism Spectrum Disorders. Journal of Autism and Developmental Disorders. 2010;40:1423–1430.
- Patterson PH. Maternal infection and immune involvement in autism. Trends in Molecular Medicine. 2011;17:389–394.
- Garay PA, Hsiao EY, Patterson PH, McAllister AK. Brain, Behavior, and Immunity Maternal immune activation causes age- and region-specific changes in brain cytokines in offspring throughout development. 2012
- Ashwood P, Van de Water J. Is autism an autoimmune disease? Autoimmunity reviews. 2004;3:557–562.
- Braunschweig D, Van de Water J. Maternal autoantibodies in autism. Archives of neurology. 2012;69:693–699.
- Fox E, Amaral D, Van de Water J. Maternal and fetal antibrain antibodies in development and disease. Developmental Neurobiology. 2012;72:1327–1334.
- Fox-Edmiston E, Van De Water J. Maternal Anti-Fetal Brain IgG Autoantibodies and Autism Spectrum Disorder: Current Knowledge and its Implications for Potential Therapeutics. CNS Drugs. 2015;29:715–724.
In conclusion, they pointed out that Maternal autoantibody related (MAR) ASD:
has been noted by numerous researchers describing the presence of maternal autoantibodies reactive to fetal brain proteins in a subset of mothers of children with ASD. Further, there is now an abundance of evidence supporting their deleterious role in neurodevelopment. For the most part, these studies have described similar experimental outcomes and, given the clinical and biological heterogeneity of ASD, there likely exists a complex relationship between the presence of maternal anti-fetal brain antibodies and developmental trajectory of exposed offspring. It is still unclear how and when these maternal autoantibodies arise, but studies currently underway may provide increased insight into their ontogeny.
Genes causing ASD
The NHS webpage on Autism states (Emphasis mine)
Most researchers believe that certain genes a child inherits from their parents could make them more vulnerable to developing ASD.
Cases of ASD have been known to run in families. For example, younger siblings of children with ASD can also develop the condition, and it's common for identical twins to both develop ASD.
No specific genes linked to ASD have been identified, but it may be a presenting feature of some rare genetic syndromes, including Fragile X syndrome, Williams syndrome and Angelman syndrome.
The NHS say that
Some researchers believe that a person born with a genetic vulnerability to ASD only develops the condition if they're exposed to a specific environmental trigger.
Possible triggers include being born prematurely (before 35 weeks of pregnancy), or being exposed in the womb to alcohol or to certain medication, such as sodium valproate (sometimes used to treat epilepsy during pregnancy).
No conclusive evidence has been found linking pollution or maternal infections in pregnancy with an increased risk of ASD.
Research Autism has some referenced information on leading research into the causes of Autism from the Medical Research Council, National Autistic Society and the Autism Society of America; and the crux of the matter from what is said here is that the causes are still being investigated and
There is no known single cause for autism, but it is generally accepted that it is caused by abnormalities in brain structure or function
The site also provides a list of publications on the possible causes of Autism
Edmiston, E., Ashwood, P., & Van de Water, J. (2017). Autoimmunity, autoantibodies, and autism spectrum disorder. Biological psychiatry, 81(5), 383-390. doi: 10.1016/j.biopsych.2016.08.031 Pubmed Central: PMC5373490