No, that is more-or-less the Jewish (and historical Christian) belief.
It was more of an issue when the Temple still stood, but the Kohain still do certain things things and face certain restrictions related to corpses and marriage.
As noted by BBL above, I would be dis-allowed as a Kohain because of my acceptance of Christ as the Messiah and am considered by several of my Orthodox family members to be a complete non-entity.
So, anyone named Cohen is a Kohain? Do all the historical restrictions and rights apply to all descendants of Aaron, or just the firstborn?
So are you what they call a Messianic Jew? Do you affiliate with any Christian denomination?