This was a question on a worksheet during my first week in a class on Electromagnetism. The answer is essentially:
No. Life would be no different if electrons were positively charged and protons were negatively charged. Opposite charges would still attract, and like charges would still repel. The designation of charges as positive and negative is merely a definition.
But how would we have negative charges within the nucleus? Taking a look at the Wikipedia page for residual strong force, it seems that down quarks are required in this new "negative proton" to help with creating the pion to "transmit a residual part of the strong force even between colorless hadrons".
I tried to set out and try to find a particle with (-1) charge with a down quark (by going through this list of baryons) but all the particles are not stable with the exception of two unknown:
Bottom Xi Baryon
Double Bottom Xi Baryon
Assuming one of the above are stable, could the strong force act between one of them and a neutron, implying its alright to have a negatively charged nucleus?
Edit: If it wasn't clear, my question concerned whether or not there existed stable baryons of $-1$ charge with down quarks that could "replace" the proton.