I often have to test a large number of cells to see if they're equal. I
usually use a-b or =a=b and check if the answer is either zero or true. If
not I know they're not equal. It would be nice if I could do this with a
custom formula that would also turn the background red, for example, if the
answer isn't either zero or true.

I doubt this can be accomplished with a custom formula, though, since
formulas are meant to return values, not "do something".