As uncomfortable as it may be, research suggests adopting an empathetic, non judgemental, but firm attitude, without any expectation to actually change their mind.
This is an attitude broadly similar to that of a professional providing advice (e.g. accountants or lawyers).
How to speak to a vaccine sceptic: research reveals what works - https://www.nature.com/articles/d41586-025-01771-z
Unpaywall:
How to speak to a vaccine sceptic: research reveals what works - https://archive.is/1gn2g