Even if minority rights do not conflict with more general ones, they may still be considered undesirable. A country with lots of immigrants may argue that, if it is to hold together, it cannot let all minorities be educated in their own tongues or promote their own cultures in preference to the national one. Were the United States to adopt that policy, it might well see the evolution of a Spanish-speaking majority in much of the west, leading in time to claims for the secession of Arizona, California or Texas.
Even the right of parents to educate their children in religious schools, which is usually regarded as basic, can have a cost. Who can doubt that it contributes to the hatred between Catholics and Protestants in Northern Ireland? School segregation by religion may be fine where religious feelings run low; where they run high it breeds divisiveness.