Let's just start with the first (and main) point.
1. They don't.
Susan in your anti-vax group is not a scholarly source (despite her hours and hours of Google research).
2. But in case you still believe Susan...
Maybe you'll believe Autism Speaks who says, "Scientists have conducted extensive research over the last two decades to determine whether there is any link between childhood vaccinations and autism. The results of this research is clear: Vaccines do not cause autism."
3. And if Autism Speaks still didn't convince you...
Feel free to take a look at this comprehensive list of studies that all say that there is no relationship between vaccines such as the MMR vaccination and the development of autism.
4. But here's what you should know...
There have been a few studies lately that have shown that autism develops in utero aka before a baby is even born AND before a baby can even receive vaccinations.
Vaccinations have prevented COUNTLESS deaths and illnesses. Vaccination rates are continuing to fall and do you know what that means? Measles will make its way back. Whooping cough will come back. Rubella, mumps, and polio will come back and there will be no way to stop it.
So, now that you know that vaccines do not cause autism, you're welcome to go tell Susan from your anti-vax group that as well as tell her that the Earth isn't flat. But, don't forget to mention it to her that her essential oils and organic foods are not keeping her children safe from the measles or tuberculosis.
Vaccinate your children. And, besides, even IF vaccinations caused autism, wouldn't you rather have a child with a developmental disorder rather than a child who died from the measles?