If protons were negative and electrons were positive, would Coulomb's Law change? Coulomb's Law is $$F=k\frac{q_1  q_2}{r^2}$$
where $F$ is the force, $k$ is the Coulomb's universal constant, $q_1$ and $q_2$ are the charges, and $r$ is the distance between the two charges.
 A: No because the law is dependent on the charges, not masses. Switching around which particle gets which charge will keep the sign on the equation the same. Opposites still attract and likes repel.
A: All of the other answers assume the mathematical theory is correct. Physics is, however, an experimental science, and looking for discrepancies between the math and reality is a constant theme.
Experimenters have created and characterized antihydrogen, with negative antiprotons and positive antielectrons. Its measured properties confirm that Coulomb's law works as expected in this case.
A: If protons were negatively charged, and electrons were positively charged, this would be equivalent to flipping the signs of all charges$^*$. Given that, it is quite simple to check that Coulomb's Law obeys charge symmetry, by applying the substitutions $q_1\to-q_1$ and $q_2\to-q_2$.
$$F = \frac{kq_1q_2}{r^2} \to \frac{k(-q_1)(-q_2)}{r^2} = (-1)^2\frac{kq_1q_2}{r^2} = F$$
Therefore, there would be no difference if we switched the sign convention of the charges.

$^*$I should note that, technically, switching the charges of protons and electrons would not be entirely equivalent to flipping the signs of all charges, since one could imagine doing this without changing the signs of the charges of other particles, like muons and pions. However, doing this would mean that, for instance, the process $\mu^-\to e^-\nu_\mu\bar\nu_e$ would become $\mu^-\to e^+\nu_\mu\bar\nu_e$, which clearly violates charge conservation.
A: Choosing positive charge for proton and negative for electron is a matter of convention, so flipping them would change nothing...
...unless we take into account other charged particles. If only the charges of proton and electron are changed, but not of the other charged particles, this may produce some unpredictable consequences... or it may not. Or it may not be possible at all from the point of view of the fundamental symmetries of the Unievrse (of which partciles are an expression).
A: Call the electrons as protons and vice versa. That's the effect your question has.
A: Signs does not matter. Only direction would change
