There appears to be some misunderstanding through parts of this thread. Some of that is a matter of how we define terms.
For example, some people define “unity” as “uniformity”. However, the Church does not define unity as uniformity, and the prime example of that is the last 2000 years of history. From the time the Apostles went out, culture played a part in, for example, liturgy. That is why we have such ancient liturgies as the Maronite liturgy, for example, and the Ruthinian Byzantine liturgy (both of which we have in Portland) as well as the Latin liturgy.
Are the different liturgies divisive? Certainly, in history, there have been implications of that. But the Church recognizes the validity of the historical approaches various cultures have taken, and John Paul 2 moved to stop the “latinization” of the eastern rites.
And within the Latin/Roman rite, we have a poster commenting about the “division” caused by having a Spanish Mass and and English Mass; it appears that his solution is to force both of them to an all Latin Mass, as if diversity were a bad word. I don’t know how far back in the Bible we need to go to show that peoples, as they spread throughout the earth, formed cultures which were different one from another. And without getting sidetracked about false worship, one can have Catholics in different cultures who celebrate the Lord’s Supper in different fashions, and yet all the same Supper.
If we have to force Roman Catholics to give up their cultures by all celebrating the Mass in Latin, in the false assumption that this makes for unity, then logically, we need to force the other 20+ Churches, all Catholic, to be Roman Catholic.
But that is only true if one presumes that diversity automatically means division (in a negative sense), and that uniformity is the same as, or synonymous with unity.
Are there divisions between cultures? Only a fool or a complete ignoramus would deny that. But the divisions are based on our brokenness which fails to see the humanness in others of a different culture. Are there people who do not want to associate with another culture? Of course there are; but that is because of their own brokenness, not because their culture is “better”, or the other culture somehow deficient. The issues between the Italians and the Polish, both Roman Catholic, in part gets to different cultures, and in part gets to tribalism. When attitudes of superiority intrude, then there is divisiveness. But wanting to worship in a Mass that has cultural aspects (such as using the vernacular of that culture) is most certainly not, in and of itself, divisive. Cultural differences can be positive or negative; and it is up to the individuals as to how they approach other cultures.
The same goes for those who consider themselves Traditional Catholics; when they step over the line form “this spirituality fits me best” to “my spirituality is superior to/better than/ more clearly Catholic than” those who prefer the OF, then it becomes divisive. When derogatory terms such as “liberal” or “modernism” are thrown about over matters which the Church allows in diversity, then division is being sown. The contempt that has been shown against those who prefer Gregorian chant, or the organ, or the fiddle back chasuble, or Latin and ad orientem is clearly divisive and not of the mind of the Church - or of Christ.
Both sides have thrown bricks; and both sides have blamed the other as having negative attitudes, and blamed those negative attitudes for the brick throwing they have done. And both sides have forgotten that when one points a finger at another, there are three pointing back.
So to answer the OP; it leads to divisions when one side or the other treats their own position as superior to the other side. It does not have to be so, but we can go clear back to Cain and Able and their differences; and human nature has not changed a whole lot since.