^((?<!.*A.*)A(?!.*A.*)|(?<!.*B.*)B(?!.*B.*)|(?<!.*C.*)C(?!.*C.*)|(?<!.*D.*)D(?!.*D.*)){1,4}$

var isValid = string.Concat(str.OrderBy(c => c)) == "ABCD";

string input1 = "ABCD";
string input2 = "ABCA";

string pattern = @"([ABCD]).*\1";

Console.WriteLine(Regex.IsMatch(input1, pattern)); // False
Console.WriteLine(Regex.IsMatch(input2, pattern)); // True

@"([ABCD]).*\1|[^ABCD]"

var isValid = !string.IsNullOrEmpty(str) && "ABCD".StartsWith(string.Concat(str.OrderBy(c => c)));

foreach(var s in new []{"ABC", "ABCD", "ABCDD"})
  Console.WriteLine("{0} {1} {2}", s, s.Length, "ABCD".StartsWith(s, StringComparison.OrdinalIgnoreCase));

ABC 3 True
ABCD 4 True
ABCDD 5 False

var valid = 
    0 < str.Length && str.Length < 5 &&  // length between 1 and 4
    str.All(c => "ABCD".Contains(c) &&   // contains only 'A', 'B', 'C', 'D'
    str.Distinct().Count() == str.Length; //  all chars are distinct

^(?:([ABCD])(?!.*\1))*$