Even people who believe in the importance of environmental causes recognise that genetics must play an important part because otherwise everyone who got exposed to certain pollutants would get autism. E.g. some people suggest that there is a genetic vulnerability to mercury poisoning. That’s almost certainly rubbish, but they still believe in genetics.

Usually when we think about causes, we tend to ascribe initiative and direction. If X caused Y, then X initiated and lead to Y. So, if I read your statement on autism being primarily genetic in this key, I conclude that genes are the driver of a disorder that is on the rise. How could autism rate increase if genes are the primary causes? Overdiagnose can be considered, mutations too, but the biggest changes around here, in the last few thousands of years, haven’t been mutations or the quality of medical diagnose, but environment.
I think this idea of genes directly and primarily causing disease has been overinflated, proportionally with the hope that was invested, and money!, in genetics. That is a big change in the environment of medical science practice and research and that can explain a lot more why autism is still thought of as a primarily genetic disorder. It’s because genetics are a major destination for funding research and universities are training more and more geneticists. Every geneticist is biased to exaggerate the influence of genes in disorder or traits.
So, I think we should forget about the primacy of genetics and focus on the interaction between genetics and environmental changes. I can quote geneticists who already stressed that genes are not “for cancer”, “for smoking”, “for gambling” etc, — rather they had a certain function that worked well in an environment they were selected for. But the big and too fast changes in environment were the ones that correlate with an increase in many disorders and diseases that we see today. On this one, I’m with Drowssap, environment must account for why largely the same genes we have with our very distant ancestors produce so many health problems today.

it would be very easy for a genetic disorder to cause infertility

Genes certainly can cause rare variants of any disorder including infertility. For a variety of reasons they can also cause regional disorders that are more common than would otherwise be expected. Of course over time these genes die out too. But I’ve never heard of a common, genetic form of infertility. That’s almost a mathematical impossibility. If you know of one lay it on me. I can see how a relatively new and isolated tribe might have something like this because of Founders Effect but this couldn’t exist in the middle of Europe or Asia unless it’s an amazing exception to the rule.
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Generally speaking genetic disorders aren’t more common than about 1 in 10,000. There are a few exceptions but most of these are still 1 in 1000 or fewer. Obviously this refers to young people. The older the age of disease onset the more common a disease gene can be.

“We’ve looked for common variants in schizophrenia and get almost nothing,” said Dr. David Goldstein, a geneticist at Duke University and one of Dr. Stefansson’s co-authors. “This means natural selection has done a really good job of purging them away, and we’re left with rare variants, a constant flow of them, as the principal driver of the disease.”

Dr. Goldstein got the first part right, natural selection works. His new hypothesis that 1% of the population has Schiz because genes are constantly mutating towards mental illness is laughable. But I guess scientists will say anything to keep their funding alive.
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All I’m getting at is that whether it’s Autism, Schiz, Cancer or anything else (especially in children) it almost always comes back to environment. People who claim it’s genes are just waiting around to be proven wrong.