In classical macroeconomics, why Labor supply responds to real wages and not money wages? real wages =  money wages/price(P).
what are the assumptions here?
why labor doesn't respond to money wages ?
To begin with, economics is all about assumptions. Because of classical dichotomy, money level doesn't impact the growth of an economy in the long run. Money has no effect on GDP in classical macroeconomics. If you want to model the effect of money, you have to introduce nominal rigidities in your model. That means, at least the goods market or the labour market is NOT perfect. If labour responds to money wages, the result would be a prefect market situation.

According to Keynes (General Theory, 1936),  the nominal wage (money wages) is completely unresponsive to current-period developments (at least over some range):$$W=\bar{W}$$
As you can see, because nominal wages are sticky, the result is an imperfect labour market. Because the labour market is imperfect, there is unemployment.  The
labor market has some non-Walrasian feature that causes the equilibrium
real wage to be above the market-clearing level.
In Keynes's model, aggregated labour supply is given. Firms are competitive and their prices are
flexible, and so they hire labor up to the point where the marginal product
of labor equals the real wage: $$F'(L)=\frac{\bar{W}}{P}$$

The main conclusion of Keynes' model is that GDP and real wages are countercyclical. Later, it was turned out to be moderately procyclical by empirical research.

Other more sophisticated models:
 - sticky prices, flexible wages, perfect labour market
 - sticky prices, flexible wages, imperfect labour market
 - flexible prices, sticky wages, imperfect labour market

If you want to model nominal effect, you should take note of nominal wages. If you are modelling fiscal shocks without the effect of the money, then considering real wages are maybe enough. It depends on one's research philosophy.