Why is there equal protons and electrons in the universe? Matter and anti-matter are asymmetric.
Why are protons and electrons symmetric?
Would we still have galaxies and stars if there were a strong overall charge? 
 A: 
Matter and anti-matter are asymmetric. Why are protons and electrons symmetric?

To start with when observing nature and modeling it mathematically one has to use the input of observations axiomatically, i.e. the mathematical model has to describe the data.
The antimatter of the electron is the positron. An asymmetry in the number of positive and negative numbers would have been observed experimentally. The elementary particle model we have that fits most data , the standard model of particle physics, posits this symmetry axiomatically by baryon number conservation and lepton number conservation. There has not been a falsification of this model, except at a small level, with CP violation which is not enough to describe the matter asymmetry observed.
So the answer is: because that is what we have observed and our mathematical model fits the data and predicts successfully new set ups.

Would we still have galaxies and stars if there were a strong overall charge?

Strong charges can happen  in the laboratory, but at a cosmological level one would have to develop a model of hadronisation  which is the way the quark gluon plasma conglomerates turn into galaxies and stars.  A different model than the standard model would be needed as the charge of quarks is an ingredient to the generation of hadrons, and an asymmetry in charges would leave free quarks which cannot exist after symmetry breaking. At the moment, extrapolating the standard model up to the times of baryogenesis works fine with all the existing observations, and there is no need to introduce complexities.
