Non-discriminating Programming
Brachylog, 10 bytes

=ᵍbᵐbᵐlᵍ=l


Try it online!

Explanation

=ᵍ                Group all equal elements together
  bᵐbᵐ            Remove the first element of each group twice. This fails if
                  there are fewer than 2 elements
      lᵍ          Group elements together that have the same length
        =         Are all elements of that list equal? This only succeeds if the
                  list has one element
         l        Length. This will always succeed