Why neglecting OH Ions from charge balance? I have a problem, in which the concentration of $\ce{Ca^{2+}}$ ions in water should be related to the partial pressure of $\ce{CO2}$ (assuming the water is an open system and in equilibrium with atmosphere).

All the approaches I saw so far, started by looking at the charge ballance of this system:

$$\ce{2 [Ca^{2+}] + [H+]} =\ce{2[CO3^{2-}] + [HCO3-] + [HO-]}$$

This is totally logical. But they continue with the assumption that the terms $\ce{[CO3^{2-}]}$,$\ce{[HO-]}$, $\ce{[H+]}$ are insignificantly small so that you can work with:

$$\ce{2 [Ca^{2+}]} =\ce{[HCO3-]}$$

That's the point I don't get. 

Assuming at the beginning there is only $\ce{CaCO3}$ and Water. Both dissociate and let's say $\ce{CO3^{2-}}$ immediatly combines with $\ce{H+}$ to $\ce{HCO3-}$, then it is reasonable that the contribution of $\ce{H+}$ and $\ce{CO3^{2-}}$ can be ignored. But what about the remaining $\ce{OH-}$? Stupidly written, I would get something like: 

$$\ce{H2O + CaCO3 } =\ce{ HCO3- + Ca^{2+} + OH-}$$

So why can I also neglect the charge caused by $\ce{OH-}$ Ions? For each bicarbonate/calcium-ion produced I would also get a hydronium ion. why can this still be ignored?
This is not totally unreasonable.

Calcium carbonate as solubility product of $K_{\mathrm{sp}} = 3.3\times 10^{-9}$ (source).

This means that if you're dissolving the solid, you'd expect a maximum calcium ion concentration of $\ce{[Ca^{2+}]} = 5.7\times 10^{-5}\ \mathrm{M}$. This is a 2.5 orders of magnitude larger than either hydronium or hydroxide concentration in neutral solution. You'd expect the carbonic acid to be mostly dissociated (at least 50%), so the bicarbonate concentration will be similar to the calcium ion concentration (maybe factor of 2 smaller).

The moment you step away from a neutral solution though, this analysis totally falls apart. You'd need more details on the assumptions of the model in that case.