StringExtensions.cs

public class StringExtensions
{
	public static string Replace(this string src, string oldValue, string newValue, StringComparison comparison)
    {
        if(string.IsNullOrWhiteSpace(src))
            return src;

        // skip the loop entirely if oldValue and newValue are the same
        if(string.Compare(oldValue, newValue, comparison) == 0) return src;

        // i'm not sure how this will work in terms of clutural comparsion, 
        // this is a hack to avoid the bug reported here https://stackoverflow.com/questions/244531/is-there-an-alternative-to-string-replace-that-is-case-insensitive/13847351#comment31063745_244933
        if (oldValue.Length > src.Length) return src;

        var sb = new StringBuilder();

        int previousIndex = 0;
        int index = src.IndexOf(oldValue, comparison);

        while(index != -1)
        {
            sb.Append(src.Substring(previousIndex, index - previousIndex));
            sb.Append(newValue);
            index += oldValue.Length;

            previousIndex = index;
            index = src.IndexOf(oldValue, index, comparison);
        }

        sb.Append(src.Substring(previousIndex));

        return sb.ToString();
    }
}

StringExtensionTests.cs

[TestFixture]
public class StringExtensionTests 
{ 
[TestCase(null, "old", "new", Result = null)]
        [TestCase("", "old", "new", Result = "")]
        public string ReplaceCalledOnNullOrEmptyReturnsNullOrEmpty(string src, string oldValue, string newValue)
        {
            var result = src.Replace(oldValue, newValue, StringComparison.OrdinalIgnoreCase);

            return result;
        }

        [Test]
        public void ReplaceGivenVariedCaseStringReplacesCorrectly()
        {
            string s = "Hello everyone from {{RecipIenT}}";

            var result = s.Replace("{{recipient}}", "John Doe", StringComparison.OrdinalIgnoreCase);

            Assert.That(result, Is.EqualTo("Hello everyone from John Doe"));
        }

        [Test]
        public void ReplaceGivenVariedCaseReplacesAllOccurences()
        {
            string s = "Hello everyone from {{RecipIenT}}. Allow me, {{reCIPIeNt}} to welcome you all to {{RECIpieNT}}'s party.";

            var result = s.Replace("{{recipient}}", "John Doe", StringComparison.OrdinalIgnoreCase);

            Assert.That(result, Is.EqualTo("Hello everyone from John Doe. Allow me, John Doe to welcome you all to John Doe's party."));
        }

        [Test]
        public void ReplaceGivenNonExistingTermReturnsOriginalString()
        {
            string s = "This string doesn't inlcude the term to be removed";
            var result = s.Replace("not-here", "whatever", StringComparison.OrdinalIgnoreCase);

            Assert.That(result, Is.EqualTo(s));
        }

        [Test]
        public void ReplaceWhenOldValueEqualsNewValue()
        {
            string s = "replace my OldValue here please. OldValue dafds fOldValue";
            var result = s.Replace("OldValue", "OldValue", StringComparison.OrdinalIgnoreCase);

            Assert.That(result, Is.EqualTo(s));
        }

        [Test]
        public void ReplaceEmptyStringWithEmptyString()
        {
            string s = "This is a string";

            string result = s.Replace("", "", StringComparison.OrdinalIgnoreCase);
            
            Assert.That(result, Is.EqualTo(s));
        }

        [Test]
        public void ReplaceWhenOldValueLenghtIsGreaterThanSourceReturnsSource()
        {
            string src = "œ";
            string result = src.Replace("oe", "", StringComparison.InvariantCulture);

            Assert.That(result, Is.EqualTo(src));
        }

        // we only really care for english, but Arabic is the only other potential possibility
        [Test]
        public void ReplaceWorksWithArabic()
        {
            string src = "الشعر في العربية شئ جميل شئ جميل ان تكتب شعر في العربية، لان شعر العربية شئ جميل";

            string result = src.Replace("شعر", "نثر", StringComparison.OrdinalIgnoreCase);

            Assert.That(result, Is.EqualTo("النثر في العربية شئ جميل شئ جميل ان تكتب نثر في العربية، لان نثر العربية شئ جميل"));
        }
  }