How can one deal with a husband who slanders people's honor and falsely accuses them without proof, and who considers his wife's defense of the accused to be a refutation of him, justifying his actions by saying it is to avoid suspicion, knowing that he becomes angry if asked to stop? And must a punishment for slander be applied to people like him, even if the accusations were true?

What your husband is doing by seeking out the faults of Muslims and being lax concerning their honor is a serious matter. He must occupy himself with what benefits him and leave what does not concern him. Your duty towards him is to rebuke him with wisdom and good admonition. If you fear a greater harm, then the duty of rebuking falls away from you, but you should leave any gathering of backbiting. His pretext of avoiding doubts carries no weight and is from the embellishment of Satan. He is not subject to a hadd punishment for what he says.