Yes, it's not cool at all, these flu shots.  When my niece was born 18 months ago, my "woke" brother told me I wouldn't be able to hold her until I'd had all my vaccinations.  I said, "Well, let me know when that dictum changes because I will get vaccinations when hell freezes over."  He did my Mom the same way and I told him and she told him essentially the same thing.  Eventually, he got over it.  Sometimes, you just gotta stand your ground, even with family.