There is a petition written on December 1, 2020 to European Medicines Agency (EMA) by Dr. med. Wolfgang Wodarg and Dr. Michael Yeadon. You can see it here. Both of them are well known for spreading misinformation about COVID-19. Yeadon used to work in Pfizer till 2011, and he is "Allergy & Respiratory Therapeutic Area expert". Some sources falsely claim that he was "head of research" in Pfizer, which was debunked by snopes.com, he was in fact a "vice president and chief scientist for allergy and respiratory".
Among other things, they want EMA to "stay the Phase III trial of BNT162" and "stay the clinical trials of all vaccine candidates [...]". "Stay" here means "to stop", I guess. They provide some reasons for why this should be done. In said petition, in section "C" ("STATEMENT OF GROUNDS") in point "XI" there is a claim about fertility:
Several vaccine candidates are expected to induce the formation of humoral antibodies against spike proteins of SARS-CoV-2. Syncytin-1 (see Gallaher, B., “Response to nCoV2019 Against Backdrop of Endogenous Retroviruses” - http://virological.org/t/response-to-ncov2019-against-backdrop-of-endogenous-retroviruses/396), which is derived from human endogenous retroviruses (HERV) and is responsible for the development of a placenta in mammals and humans and is therefore an essential prerequisite for a successful pregnancy, is also found in homologous form in the spike proteins of SARS viruses. There is no indication whether antibodies against spike proteins of SARS viruses would also act like anti-Syncytin-1 antibodies. However, if this were to be the case this would then also prevent the formation of a placenta which would result in vaccinated women essentially becoming infertile. To my knowledge, Pfizer/BioNTech has yet to release any samples of written materials provided to patients, so it is unclear what, if any, information regarding (potential) fertility-specific risks caused by antibodies is included.
According to section 10.4.2 of the Pfizer/BioNTech trial protocol, a woman of childbearing potential (WOCBP) is eligible to participate if she is not pregnant or breastfeeding, and is using an acceptable contraceptive method as described in the trial protocol during the intervention period (for a minimum of 28 days after the last dose of study intervention).
This means that it could take a relatively long time before a noticeable number of cases of postvaccination infertility could be observed.
I understand that this two gentlemans are not very credible. But is it true, that there is a significant chance that antibody response against spike proteins of SARS-CoV-2 could result also in antibody response against syncytin-1, which is important in formation of placenta and then basically would cause intertility of unknown duration? I know that we are never 100% sure with things that complicated, but is it a valid concern scientifically, or something very unlikely and he just abuses the fact that he found some connection between spike protein of SARS-CoV-2 and human placenta?
In other words: does the authors of this petition ommited some important difference between antibody reaction to SARS-CoV-2 spike protein and reaction to syncytin-1 that is forming human placenta? Something that could be use to ease people's minds, that was taken into consideration by teams developing SARS-CoV-2 mRNA vaccines?
Another way to put this in question would be: what are the chances that antibodies against spike proteins of SARS viruses would also act like anti-Syncytin-1 antibodies?