The VA gave me the J&J jab in March of 2021. By July of that year they wanted me to take Pizer vaccine. No.
I have politely declined each time my VA PCP recommended it. I will likely take the flu shot this upcoming season, just because I got it last month and it was a real slog getting over it (temp of 103.8 for 3 days, 3 weeks to feel right again).