If we all go through life thinking that no-one should ever be rehabilitated back into society or have the right to a life of any kind after committing one offence then we might as well write off the idea of restorative justice and sentence all criminals to death.
Everyone has the right to make their own decisions about the people they become involved with but equally people are able to change or even to move on from their past in order to live decent lives after what they have done.
We don't know the circumstances of this man's crime. Manslaughter just isn't a black and white crime as it is, it's horrible to think that one person could kill another but equally different circumstances can lead to different outcomes.
If you e.g. Look at someone like Louise Woodward who was convicted of manslaughter for killing a baby in her care in the US, she is now living back in the UK and iirc has children of her own now. And as far as I'm aware is not involved with SS and has presumably managed to have a successful relationship given she has children. Personally I couldn't get involved with someone who had killed a baby but others clearly don't think the same as me. And presumably as it was manslaughter she didn't intend to kill him, but different people's views would depend on where she was accepted in society.
Similarly there are people who would run a mile from a man who was involved in a fight where someone died. But there are others who might have listened to the circumstances and believe that he has turned his life around, or even that he was never a bad person in the first place but regrets what he did.
And equally there are people who would judge the crime but not the individual who committed it, i.e. He might be lovely but one might feel it impossible to be intimately involved with someone who had killed someone. I think I would fit into that category tbh. I could possibly accept someone as a friend who had been to prison but who had regretted their actions and moved forward, but couldn't personally be in a relationship with them. But other people have a different view, and others in turn decide that even the actions render the individual an evil bastard for life. Judgement is subjective, and often there is no right or wrong.
Personally I would find out the details, not from him but from public records, and then decide how to proceed.
And I understand your dad's view but equally demanding that you end the relationship is just as controlling - he should seek to explain his issue rather than throwing around demands which will achieve nothing. You're an adult, capable of making your own decisions and even mistakes......