A convert can marry a king. A convert can marry a prophet. A convert can even marry a rabbi, the highest echelon of Jewish society (if you ask me :). So it makes no sense to say that a convert can’t marry a cohen because they are second class citizens. There must be some other reason.
Here’s a thought for your consideration:
When the Torah forbids a marriage, it is never because one party is not good enough for the other. It is because both parties are not matched to each other. They are simply not soulmates. In the case of the cohen and the convert, their soul dynamics clash, their spiritual energies contradict, and so they can’t marry.
The holiness of a cohen is hereditary. If your father is a cohen, then you are a cohen. Priesthood is a birthright that is not achieved through a person’s effort nor deserved through a person’s righteousness. It is an honor that is bestowed at birth.
The holiness of a convert is the exact opposite. It is completely earned. The convert was not born Jewish. They chose it. They achieve Jewishness of their own initiative and with their own hard work. They are self-made souls.
So these two souls, the cohen and the convert, are moving in opposite ways. The cohen receives their power from above. The convert creates their own soul energy from below. The cohen has the ability to bring down blessings to others, just as their soul was given to them as a blessing. The convert has the power of innovation, of initiative, of creating holiness from the ground up. They are going different directions. For this reason their souls are not a match.
Both the cohen and the convert have awesome holiness. It is a great privilege to be gifted with the soul of a cohen. And yet, the self-made soul of a convert has a depth of experience that inherited holiness cannot compete with. Neither are second class souls.
The cohen is crowned with a legacy from past generations. A convert creates their own legacy for future generations. The Jewish people is richer for both of them.
Rabbi Mendel Bluming and Rabbi Moss