The attempt by some Republicans to smear Obama as some sort of "anti-colonialist" is deeply bizarre for two reasons. First, it's not based on any facts; second, it suggests that being opposed to the exploitation and bloodshed of colonialism is somehow a bad thing.
The anti-colonial accusation is at the heart of far-right talking head Dinesh D'Souza's light-on-facts, heavy-on-paranoia film 2016: Obama's America. D'Souza has been beating this drum for a while; he seems to believe that Obama became President as part of some plot to destroy American in revenge for its colonial sins. (Or, quite possibly, he does not actually believe this tripe but knows it will rile up the racist and nationalist elements in the GOP base.)
Now it seems to me pretty bizarre to accuse someone who has kept U.S. troops occupying foreign lands for almost four years, and has claimed the imperial power to designate people for death without trial, review, or any legal process at all, as some sort of grand opponent of colonialism. He might be less of a proponent of it than D'Souza and his ilk, but like every other Americans president of the past century and half or so, Obama is a colonialist who sees the main purpose of the world outside the U.S. as being to serve American interests.
As Lamar W. Hankins notes,
...An anti-colonialist would have already ended the occupation of Iraq and Afghanistan by American military forces. An anti-colonialist would not have joined NATO in the bombing of Gaddafi’s forces in Libya. An anti-colonialist would not be using drones regularly in Pakistan, Yemen, and elsewhere. An anti-colonialist would not be continuing the decades-long involvement of this country in Colombia. An anti-colonialist would not maintain the 50-year embargo against Cuba. An anti-colonialist would not be funding the expansion of military bases in the Middle East. An anti-colonialist would not continue funding the wide-spread violation of human rights by the military in Colombia. An anti-colonialist would not be maintaining 900 military installations in 130 countries around the world. An anti-colonialist would not be expanding the military, whose primary use historically has been colonial expansion on behalf of American commercial and economic interests.
D’Souza, Gingrich, Ricketts and all the other anti-Obama zealots seem incapable of seeing Obama for what he really is – a mainstream, American exceptionalist with a colonialist mentality. Every president in my lifetime has pursued a colonialist agenda, some more than others. Obama fits right in the middle of this group – not the most expansionist, but not anywhere close to being the least expansionist. Unlike the earlier colonialism, where we actually controlled the apparatus of government in other countries, we now use our military might and economic leverage (directly and through the World Bank and the United States Agency for International Development) to control the policies of other countries. None of this has changed under Obama.