C# string comparison ignoring spaces, carriage return or line breaks

You should normalize each string by removing the characters that you don’t want to compare and then you can perform a String.Equals with a StringComparison that ignores case.

Something like this:

string s1 = "HeLLo    wOrld!";
string s2 = "Hello\n    WORLd!";

string normalized1 = Regex.Replace(s1, @"\s", "");
string normalized2 = Regex.Replace(s2, @"\s", "");

bool stringEquals = String.Equals(
    normalized1, 
    normalized2, 
    StringComparison.OrdinalIgnoreCase);

Console.WriteLine(stringEquals);

Here Regex.Replace is used first to remove all whitespace characters. The special case of both strings being null is not treated here but you can easily handle that case before performing the string normalization.