For example, I strongly support those states in the USA that have implemented requirements that children have received certain vaccines to be able to register in schools, subject to limited exemption rights. The doctrine in those states (California, following a fatal measles outbreak, is one) is that the risks to others from not being vaccinated significantly outweighs the benefits of allowing complete parental freedom of choice. Where the benefit of the vaccine is both personal (having received it, I will be protected from the disease) and collective (if I don't get it, that significantly protects others), this seems a reasonable trade off between personal and collective freedoms; I wouldn't take the same view of (say) a Tetanus jab because the benefit is fundamentally personal.
As for the question of those in the public eye, it is a difficult trade-off. In the case of the Blairs (remember, it was their action, not that of their baby son, that was central), I consider it fell the wrong side of the line because it was a situation in which the PM failed to back the policy of his government. In Corbyn's case, I agree that there is some difficulty when he's been asked the question, and it's obviously being used to attack his credibility. If the answer was "no comment", I'd have had no issue; the plea for privacy has a strong whiff of equivocation around it which is what I struggle with and where I strongly suspect a lack of moral courage to declare a position.
Ultimately, though, my view is that receiving a generally available vaccination against transmissible disease is not just a private matter; it has a public element because the effect of vaccination for a transmissible disease is public, not just private.