C (gcc), 176 333 168 bytes
Thanks to @Kevin Cruijssen for saving 9 bytes and thanks to @Laikoni for saving 45 bytes!
f(r,nh,a){char*h=rchar*o=r,c[222]={!ho};for(a=!h;*h;o;*o;)++c[*h++];for++c[*o++];for(n=h=!h;222o;222/++n;c[n]&&c[n]++h;c[h]&&c[h]!=a&&(a=!*c))!a&&c[n]&&a&&c[h]&&(a=c[n]a=c[h]);r=!(2/2/a);}/////!(())****++,,,,,[[]]fffffhnoooooorr[[]]fffffrr{{{{{{}}}}}}
C, 333 bytes
i,v;f(S){char*s=S,L[128]={0};for(v=0;*s;)++L[*s++];for(i=-1;++i<128;L[i]&&L[i]-v?v=-1:0)!v&&L[i]?v=L[i]:0;return-v<-1;}/////////!!!!!!!!&&&&&(((((())))))******+++,,,,,,,----00000111122222228888888:::::::<<<<<<<===???????LLLSSSSSSS[[[]]]aaaaaaaacccccccceeeeeeeeffffffhhhhhhhhiinnnnnnnnooooooorrrrssssssttttttttuuuuuuuuvv{{{{{{{}}}}}}}
Even the bytecount is non-discriminating!