C# – In C#, why is String a reference type that behaves like a value type

As others have said, it will only work when T is constrained to be a reference type. Without any constraints, you can compare with null, but only null - and that comparison will always be false for non-nullable value types.

Instead of calling Equals, it's better to use an IComparer<T> - and if you have no more information, EqualityComparer<T>.Default is a good choice:

public bool Compare<T>(T x, T y)
{
    return EqualityComparer<T>.Default.Equals(x, y);
}

Aside from anything else, this avoids boxing/casting.

You could use the String.IndexOf Method and pass StringComparison.OrdinalIgnoreCase as the type of search to use:

string title = "STRING";
bool contains = title.IndexOf("string", StringComparison.OrdinalIgnoreCase) >= 0;

Even better is defining a new extension method for string:

public static class StringExtensions
{
    public static bool Contains(this string source, string toCheck, StringComparison comp)
    {
        return source?.IndexOf(toCheck, comp) >= 0;
    }
}

Note, that null propagation ?. is available since C# 6.0 (VS 2015), for older versions use

if (source == null) return false;
return source.IndexOf(toCheck, comp) >= 0;

USAGE:

string title = "STRING";
bool contains = title.Contains("string", StringComparison.OrdinalIgnoreCase);