When people exhibit having dual beliefs that are opposites, putting people, in effect, in conflict with themselves, is it always the case these beliefs reside within differing levels of the mind? Or is it the case that subparts of the mind on the same level can simply hold differing views?

It is more the case that you are dealing with differing levels of the mind. The exception is in people with severe trauma who have fragmentation of the self and identity into subpersonalities. This is also done willfully through mind control manipulation to cause a Dissociative Identity Disorder manifestation for purposes of exploitation as an operative of some kind, when subparts of the self can be groomed to participate in dark doings and then remain unobserved by the higher levels of the mind, and can thereby remain a secret part of the person, and all the doings will be suppressed from conscious awareness. This makes a perfect spy or saboteur because any illegal conduct, even when caught in the act, will be denied with a straight face, and the person will be able to profess innocence quite convincingly and will, moreover, be prepared with cover stories that will often gain their release because no one would presume such an elaborate preparation and sinister capability being possible to deliberately create, in effect, a mind controlled slave. But yet, this is done over and over again by many people with the training and know-how to exploit others in this way.