As long as you keep the Head of Government away from the sovereign, presidents can be harmless enough to avoid this kind of polarisation. Maybe look at Ireland

As long as you keep the Head of Government away from the sovereign, presidents can be harmless enough to avoid this kind of polarisation. Maybe look at Ireland or Portugal as examples of republics where the president keeps the constitutional safeguards (dissolving parliament, vetoing laws, and what not), and you'll see that they are not exactly polarizing figures. Instead, the prime ministers are, as they should (they head partisan politics).