it might be better for either side to put forth more moderate candidates for head of state. Send the revolutionaries to the legislative branch, lol.

This is because whenever one side wins an election, there tends to be a 'backlash' and minimizing the polarity of that backlash is less traumatic for all involved.

In the US, there's a natural check-and-balance built into congressional representation (eg. it's bicameral, frequent election cycles in the lower house, etc) and progressives are actually quite empowered there by the ability to put forth legislation. It's on them to try and win support from the rest of the chamber to have it pass.

But head of state is one person with super high visibility. Better for that person to be stable and not crazy, embarassing, authoritarian, etc to a large segment of the population or the international community, imo.