When someone's immune system is severely compromised, they can succumb to anything. Including a vaccine which works by stressing the immune system. As with any drug/vaccine/medical test or procedure, it's a matter of personal choice. Nothing whatsoever to do with responsibility or protecting others.
Many people who try to convince others to get a vaccine are seeking confidence in their decision to get it - Confidence in numbers.
And if people who choose the vaccine had confidence in it, it wouldn't matter to them if others didn't choose to get it, since they would be protected.
We see the same mindset in other health issues - People who choose to have colonoscopies & other medical tests often try to convince others to have them. They're looking for validation for their decision.