By my understanding their charge could have been called positive, and the charge of the proton and positron called negative. What are the historical reasons for this?
When they discovered electricity they were studying electric current. They called this a positive flow of charge, because it's in the direction of the current that they saw.
When they discovered the electron they found that it was moving opposite to the previously determined "positive" flow, therefore calling it negative.
When they discovered the proton they realized that it's attracted to electrons. Since electrons are "negative" they called protons "positive".
They're arbitrary naming conventions that have nothing to do with any actual physical properties of the particles.
You could switch them and as long as you maintain that switch on all your calculations then it all still works out.