I'm writing a compare/contrast essay. I have to identify the similarities and differences between two characters. Should my thesis statement...

Generally, I would say you should include the points of comparison and contrast in your thesis statement. Otherwise, you get a thesis statement like this:

In The Great Gatsby, Tom Buchanan and Jay Gatsby are similar to one in other in some ways and different in others. 

You can see that is not a particularly informative or impressive statement. It does not give the reader a clue what you are going to say, and...

Generally, I would say you should include the points of comparison and contrast in your thesis statement. Otherwise, you get a thesis statement like this:

In The Great Gatsby, Tom Buchanan and Jay Gatsby are similar to one in other in some ways and different in others. 

You can see that is not a particularly informative or impressive statement. It does not give the reader a clue what you are going to say, and a thesis statement is meant to provide the reader with a workable outline of what is to follow.  This kind of statement also has the drawback of not making the reader all that interested in what you have to say, what we call the "So what?" factor.  That factor does not necessarily have to be in the thesis statement, but it works wonderfully well if it is. 

Now I will say that if you have a great many points to make about similarities and differences, you can end up with a long and clumsy statement, which you will want to avoid.  In a situation like that, the best thing to do is to place all the points into two or three discrete categories.  For example, I might say this about Daisy Buchanan and Myrtle Wilson (also from The Great Gatsby):

The differences and similarities of Daisy Buchanan and Myrtle Wilson, neither of them particularly likable, are reflected in their socioeconomic classes, their physical appearances, and their priorities. 

I have listed some general categories, and within each, I can pursue more than one point about similarities and differences.  I have also provided a kind of "So what?" element, as I make clear to the reader that these are not very likable women.  This is really my main idea in the thesis statement, with my supporting categories as my points.  If I were to list ten or twelve points of comparison and contrast, I would have a sentence that would not be easily navigable by the reader. Also notice that I have not designated which categories are about differences and which are about similarities, which leaves me free to pursue either or both in any of the categories I have listed.  

All in all, it is always best to include your points of contrast and comparison, at the very least, lumping them into a few categories that will cover all of them. If you can include your "So what?" element in the thesis statement, that is even better.