A worldview is basically a series of propositions that may accurately reflect reality. An adherent is one who holds those beliefs. In conversations about reality, a worldview may be addressed; the adherent to a worldview may be addressed, or both may be addressed. When addressing a worldview, one takes its propositions and tests them against reality. There are multiple levels of worldviews that get more specific. Within the theistic worldview, you have Judaism, Christianity, Islam, and others. Within the Christian worldview, there exists Calvinists, Arminians, Compatiblists, etc. And there are more divisions at the same level of that with other distinctions. The general worldview or the specific worldviews may be tested. I expand on this more in my post "Can Religion Be Tested For Truth?".
However, here we are only addressing the worldview, not the adherent or person who claims it. Addressing a person tends to be more on the difficult side. A person may not be completely committed to a single worldview in profession or in practice. Some try to take propositions and practices from multiple worldviews. A worldview, itself, can be addressed dispassionately- you demonstrate an inconsistency either internally or externally (with reality), and its done. However, those who hold the worldview that was just shown inconsistent, may not abide by the conditions of the inconsistency. Ultimately, a person is not required to maintain consistent beliefs and practices. They may hold inconsistent beliefs and act inconsistently with their worldview.
This is where getting to know a person and understand their particular views will come in handy. If we are to address a person, we cannot just assume that they hold a specific worldview. We may be using concepts to show an inconsistency that they don't even accept as true. Unless the concepts (premises in an argument) are accepted by both parties, then both parties are not going to accept the inconsistency (conclusion in the argument). I discuss this more in my post "Misengaged in Battle".
We also cannot forget that people are not dispassionate robots. Just because we input a few premises, we cannot always expect them to output the right conclusion. People have emotions that cause them to hold passionately to certain beliefs. Even in the face of a sound argument, they may still deny the conclusion. Emotions also speak quite loudly in the middle of adverse circumstances, and arguments may be the last thing they need (Carson Weitnauer at Reasons for God posted on this: Arguments That Hurt).
Finally, just because someone believes that a worldview is true, it does not mean that they will dedicate their life to it, or just because they believe that a personal God exists, that they want a relationship with Him, or that if they believe that Jesus Christ offers a gift of salvation that they will accept it. I go into more detail about this last issue in my post "Can You Argue Someone Into The Kingdom?".
There is a distinction between a worldview and the one who holds it. Both are different and must be addressed differently. Many times it is difficult to separate the two, whether on the giving or receiving end. It is the responsibility of the giver to distinguish, and the responsibility of the receiver to discern the distinction. We cannot rely on the other to always do their part, so we should make sure that we are doing our part.