You can’t have unity without equality.
Sure you can. Look at a good basketball team for example. Some players are really tall, others are shorter but fast, some may play 40 minutes while others might not make it off the bench. None of these players are equal because they are different. But they all play an important part, and all are unified together in a goal to win basketball games.
They all received a scholarship. (Kind of like how we all have the same rights protected by the constitution.) The success of the player after that point depends on a combination of natural ability, work ethic, and desire. Same way for Americans in every day life.