Must faith schools be divisive?

Segregation divides societies and that some British cities are segregated by religion as much as by race. Does this mean that faith schools are inherently divisive, or can they overcome some divisions even if they tend to exacerbate others? Is there anything about the teaching of a religious ethos that tends to divide societies more than an irreligious one, perhaps based on class or nationality? Is there an alternative that is politically workable?