From the FullFact link given above (my bolding).
No evidence Pfizer Covid-19 vaccine affects women’s fertility
fullfact.org/health/vaccine-covid-fertility/
^Where did this claim come from?
The origins of this claim stems from a protein on the surface of the SARS-CoV-2 virus (the virus which causes Covid-19), called a spike protein. This spike protein helps the virus enter cells and is also one of the ways the human body recognises a virus and knows to let its immune cells attack it.
The Pfizer vaccine works by giving the body the instructions on how to make this spike protein, so it can generate an immune response that attacks the virus via the spike protein faster and more effectively if it is later infected.
The building blocks of proteins are called amino acids, and it’s sequences of those that make up different proteins.
A small part of this spike protein resembles a part of another protein vital for the formation of the placenta, called syncytin-1. But the sequence of amino acids that are similar in syncytin-1 and the SARS-CoV-2 spike protein is quite short.
But only two very small parts of these proteins look the same—it’s not the whole protein—and therefore realistically the body’s immune system is not likely to confuse the two, and attack syncytin-1 rather than the spike protein on SARS-CoV-2 and stop a placenta forming.
What do the experts say?
Virology professor Ian Jones at the University of Reading told Full Fact, via the Science Media Centre, that the spike protein and syncytin-1 don’t look similar enough for the same antibodies that the body would create as an immune response to the vaccine, to bind to and attack syncytin.
He said syncytin-1 is “completely unrelated to the SARS [spike] protein” and the risk of infertility is “therefore essentially fictitious.”