At the risk of sticking out on my own here, I actually would be offended if someone asked that of me, and I do think it's unreasonable to do so. People may have good reasons why they don't want the booster - actually, they don't even need a good reason - in this country, vaccination is not compulsory.

HOWEVER... I can totally understand where you're coming from, having walked a very difficult journey with your friend. So if that's what you want to do, as the parent of your baby you are perfectly entitled to make that rule. Just be prepared for people to be offended, and work out a response that doesn't inflame the situation eg "I'm sorry you are upset, but please understand after knowing a baby who died from this, it is important to me".

Hope I didn't offend anyone - just my humble opinion!