(1) "doctors didn't know for sure" - that is a usual state for a doctor - e.g. 'the symptoms of this patient strongly suggest x, but it could also be y or z. Given the data, the best course of action is ...'. Do you imagine that a doctor even today, examining a patient with e.g. persistent headaches, or chest pains, or ..., knows 'for sure'?
(2) I am not a medic. But a few times I have helped people in critical condition (accidents etc) - in all cases, I did my absolute best to save the persons' lives. If paramedic's had shown up saying 'you xxxxing idiot, you ought to be doing xyz' I would have been happy to accept their advice, no matter how they 'presented' it. I hope you would also.
(3) In farming work in the past, I have often made mistakes (either ignorance or error) when caring for animals, sometimes those animals died due to my mistakes. Being told 'you xxxx xxxx why didn't you do xyz' afterwards, meant that I did better next time. I sure as hell didn't think 'oh, I don't like the way that is being presented, I think I'll just ignore it'.
To be clear, I am condemning the doctors of the time.
I am not necessarily disagreeing with you about whether or not Semmelweis could have been more tactful - I don't know enough to really comment (e.g. it might be that he was tactful initially, but as time went on and he was ignored, he 'turned up the volume').