In a sense yes, but the word 'many' is potentially confusing. The implication is that it is more than expected and so far I don't think there is evidence for that. Things are going to be loaded one way or another. Unnecessary concerns about vaccines may well kill something like 500,000 people in the USA in the end.
I hear you, and the points you are making are important. However, I don't agree that "the implication is that it is more than expected". To me "many" is a neutral enough word in this context. Looking at the actual numbers of reports, it doesn't seem to be an awfully rare reaction. Would you feel more comfortable if we use the word "some" instead?
As mentioned already in this thread, there is so much stigma around menstruation and so called "women's health" problems, and a very long history of medical neglect, abuse etc too. That's one of the reasons why it irks me when people are immediately trying to minimise and/or explain away these things, even attempting to shut down discussions about it on some platforms -- in the context of vaccines or not, regardless.
I personally haven't seen anyone use the fact that this is happening to "some" women as a tool to try and discourage others from having the vaccine. The way I've seen it expressed on social media is just a simple agenda-less sharing of personal experiences, and to let others know they are not alone in experiencing the same. It really means a lot to many ("some") of the people affected, to simply know that they are not alone, and to feel free to discuss intimate issues like this openly without being silenced or having their experiences minimised or politicised by others.
The
Swedish news stories I've read have been neutral too, simply stating that so far this many reports have been made, and as of yet it's not confirmed whether they are vaccine related reactions or not.
Here's an example of
a Danish article on the same.
In the interest of full transparency, this is personal to me, too. I suffered from continuous, very heavy bleeding for more than 6 weeks at one point not long after I came down with ME. I was repeatedly denied medical assessment, and instead offered only CBT to "help manage my worry". It was an horrendous experience to have to go through, and I was completely alone. My ME onset happened to be vaccine associated (not covid).
I'm asking you to please be sensitive to the larger context in which this discussion is happening, and the stigma surrounding so called "women's health". Please.