Colonialism continues to impact Latin American politics in at least two ways.
First of all, in many places, there is still a "white" political elite. The dominance of this elite is a legacy of colonialism. We can see this, for example, in the fact that Evo Morales of Bolivia gains much of his support from taking the cause of indigenous people against the white elite.
Second, defiance of outside interference is a potent theme in Latin American politics. A leader like Fidel Castro (or Hugo Chavez) can make a career out of using animosity towards the United States as a theme. Such leaders can position themselves as people who will defiantly stand up against the US and its attempts to interfere in the region in a neo-colonial way. Because the region has been subject to colonialism and neo-colonialism, this is a potent stance to take.
In these ways, colonialism continues to affect who is in power in Latin American countries and the kinds of postures they take in order to appeal to their people.