sure - if the public stays divided they may be less likely to push for policies that could reduce inequality, like higher taxes on the wealthy, better labour protections, regulation of large corporations. If people see each other as the problem, they pay less attention to systems or policies that are keeping them poor.
basically, if two neighbours spend all their time arguing about who belongs in the neighborhood, they may never notice that both of their rents keep rising or that their wages haven't kept up with living costs.