re: What does it mean that God gave them over to their sins?

Dracula doesn't mind the Cross itself so much. His disdain is directed towards those who would brandish the Cross directly in the face of Non-Christians in an attempt to make them feel bad about themselves. Dracula is opposed to this kind of exclusionary and mean Christian behavior.

IMHO, all of the Dracula movies have been misinterpreted, because they don't emphasize this fact.

Dracula is a Democrat for Freedom of Religion. He doesn't like to see the Cross to be used to push religion on anybody. That's why he gets upset when Dr. Helsing brandishes the Cross at him. Helsing's behavior stems from Crusaderism and Colonialism, and Dracula is vehemently opposed to both of these White Supremacist characteristics of Western Culture.