Which other issues are matters of personal conviction to Democrats?

Can a Democrat be personally in favor of waterboarding?
Can he be personally in favor of police brutality?
Can he be personally in favor of castrating rapists?
Can he be personally in favor of abolishing Medicaid?
Can he be personally in favor of releasing sulfur dioxide into the environment?
Can he be personally in favor of dropping a hydrogen bomb on Teheran?
Can he be personally in favor of abusing animals?

Or is it just women's rights that a Democrat can be personally in favor of violating?