Antivax immunologist J. Bart Classen published a paper claiming that mRNA-based COVID-19 vaccines can cause prion disease leading to neurodegenerative diseases like Alzheimer's dementia. What are prions, and can these vaccines cause prion disease? (Spoiler alert: The answer to the second question is almost certainly no. It's speculation based on highly implausible biology.)
Antivaxxers have been claiming that vaccines cause female infertility for as long as I can remember. So it's not surprising that they are now claiming that COVID-19 vaccines will cause miscarriages or even make women infertile. Their assertion is based on a highly speculative and incredibly unlikely immunologic mechanism. Same as it ever was.
During the COVID-19 pandemic, there hasn't just been a pandemic of coronavirus-caused disease. There's also a pandemic of misinformation and bad science. It turns out that doctors today are just as prone as doctors 100 years ago during the 1918-19 influenza pandemic to bypass science-based medicine in their desperation to treat patients.