How to not include line breaks when comparing two strings

A quick and dirty way, when performance isn't much of an issue:

string1.Replace("\n", "") != string2.Replace("\n", "")

Assuming:

1. The sort of direct char-value-for-char-value comparison of != and == is what is wanted here, except for the matter of newlines.
2. The strings are, or may, be large enough or compared often enough to make just replacing "\n" with an empty string too inefficient.

Then:

public bool LinelessEquals(string x, string y)
{
    //deal with quickly handlable cases quickly.
    if(ReferenceEquals(x, y))//same instance
        return true;         // - generally happens often in real code,
                             //and is a fast check, so always worth doing first.
    //We already know they aren't both null as
    //ReferenceEquals(null, null) returns true.
    if(x == null || y == null)
        return false;
    IEnumerator<char> eX = x.Where(c => c != '\n').GetEnumerator();
    IEnumerator<char> eY = y.Where(c => c != '\n').GetEnumerator();
    while(eX.MoveNext())
    {
        if(!eY.MoveNext()) //y is shorter
            return false;
        if(ex.Current != ey.Current)
            return false;
    }
    return !ey.MoveNext(); //check if y was longer.
}

This is defined as equality rather than inequality, so you could easily adapt it to be an implementation of IEqualityComparer<string>.Equals. Your question for a linebreak-less string1 != string2 becomes: !LinelessEquals(string1, string2)

I'd suggest regex to reduce every space, tab, \r, \n to a single space :

Regex.Replace(string1, @"\s+", " ") != Regex.Replace(string2, @"\s+", " ")