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Tipping is not the issue. Racking is the issue. The base would stay put but from there up it would tilt/bend. Why not put a plywood back on it? It would solve the racking problem and also keep your wall from getting dinged up when you put things on the shelf. It doesn't have to be thick plywood. Even something as thin as paneling would do the trick. At least put some 45 degree gussets in each corner of the back. Like maybe 6" x 6".

As far as making the cuts square, how will you be cutting them? A handsaw? If so, the best you can do is draw a line with a square and follow it as best you can. If you are using a circular saw, put a square on the shelf board, then clamp a 1 x anything against the square in the right spot so you can put the saw base against it while you make the cut.
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