Was there ever a different type of government in Mexico before now?

Answer 1

Yes:

• From 1821 to 1823 it was an absolute monarchy, officially known as the First Mexican Empire, led by Agustin de Iturbide.
• In 1823, several generals staged a coup d'etat against Iturebide, switching to a Federal Republic. It stayed as such for the first half of the 19th century
• In 1864, French forces invaded Mexico, temporarily setting a monarchic protectorate led by Maximilian I of Habsburg. This is known as the Second Mexican Empire.
• In 1867 Mexican forces led by Benito Juarez gained the upper hand during such invasion, finally defeating the French an reestablishing the republic, which has continued to this day.

Answer 2

There were two periods when Mexico became an Absolute Monarchy. Once between 1821 and 1823, right after independence from Spain; the other between 1864 and 1867 thanks to a puppet government installed by French invaders. The rest of the time, Mexico has been a federal republic.