Very thoughtful point. I was concerned about it as well. Rushing a half-backed vaccine that has serious side-effects will fuel antivaxxers for decades.
There has actually been something like this during the swine flu pandemic. There was a vaccine that is believed to have caused some cases of narcolepsy. This was a real, bad sideeffect with a vaccine that was rushed to market.
Surprisingly this isn't a big talking point in antivaccine circles. Yeah you'll hear about it sometimes, but compare it to the number of times you hear "somethingsomething MMR aluminium autism" which is all debunked bullshit - you'll hear that far more often.
What I want to say is: Antivaccine people largely don't care about real issues with vaccines. They're happy with their pseudoscientific nonsense, that's good enough for them to reject every vaccine ever made.