So the study, which appears in JAMA Pediatrics, does indicate that children born to moms who took SSRI drugs during their second and third trimesters may be slightly more likely to have autism.
The study looked at pregnancies and children in Québec over a ten year period. It is a cohort study, meaning that it observes a whole bunch of data looking for a correlation between one factor and another.
No matter how good a cohort study is, it can only show correlation. Which might mean there's causation, but might not. For instance, I'm far more likely to be accosted by a giant spider after eating a Vegemite sandwich, not because Vegemite causes spider attacks, but because I'm more likely to encounter both while visiting Australia.
So while it could absolutely be that SSRI drugs cause autism in fetuses, it might also be that moms who are under the care of a psychiatrist are more likely to take their kid to a psychiatrist (the study might have controlled for that, but I'm not paying the $30 bucks required to see the full methodology).
So the only thing a cohort study can do is say whether a correlation is or isn't present, and indicate whether more research is warranted.
A couple of other factors to consider before dumping those drugs down the toilet: the average kid in the non-SSRI group had a .7% chance of being diagnosed with autism, versus 1.2% in the SSRI group, so even though 1.2% is, in fact, 87% more than .7%, we're still only talking about one out of every hundred kids. In addition, there have been many other studies looking for a correlation between psych meds and autism, and none of those have found one.
Does that mean SSRI drugs are perfectly safe to take when you're pregnant? It most certainly does not. There are all kinds of possible side effects, some serious. However, mental illness / mood disorders can be really dangerous for a developing baby too, so mom and her doctor have to weigh the risks and benefits very carefully. Which makes it not so responsible for people who don't know what they're talking about to run around screaming about the autism apocalypse.
If you're really worried about a pregnant lady in your life poisoning her baby's brain, the more responsible thing to do would be to maybe suggest she talk about the risks of SSRI use with a doctor or two. Because one thing the overwhelming majority of research does tell us is that excessive stress in mom can cause serious issues in a developing baby.