I don't know on what all (every single one) anti-vaxx beliefs are based, which is why I generalized based on my experiences with the beliefs I've encountered. I can't readily form an opinion on a belief I haven't encountered, can I? All of the common anti-vaxx talking points fit the criteria I listed above, and I know this from my experiences reviewing and researching them. So yes, it is a good idea to generalize for the sake of conveying my experiences here, though I'm not going to prejudge any new anti-vaxx views I haven't previously encountered.
From what I have explored, those beliefs are based on misinformation or misunderstandings drawn from scientific research. In contrast, the vaccine orthodoxy is drawn from a strong body of evidence "where trials and statistics matter". If you are going to assert otherwise, then please provide specific examples.
And additionally, would you think it is a good idea to generalise here?