sub is_rotateable{
  local $_ = shift;
# Shave two
#  y/23467/5XX9X/;
#  return 0 if /X/;
  y/26/59/;
  return 0 if /[347]/;
  @_ = split//;
  while( @_ > 1 ){
    return 0 unless shift == pop;
  }
  return 1;
}
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UPDATE: FYI That's 122 including the sub, 102 without. OP was 281 less the whitespace though some easy shavings existed such as s/=>/,/g.