No, he is not. Fascism is defined by Merriam-Webster as "a political philosophy, movement, or regime...that exalts nation and often race above the individual and that stands for a centralized autocratic government headed by a dictatorial leader, severe economic and social regimentation, and forcible suppression of opposition".
While Barack Obama's tenure as president could be considered corporatist and certainly right-of-center, his administration did not exemplify the totalitarian and hyper-nationalistic tendencies of a fascist regime.
President Donald Trump's administration, on the other hand, has been flirting with fascism since before he took office. Using the phrase "America First" to echo Nazi sympathizers from the 1930s, blaming immigrants (from very specific types of countries) for complex issues, quoting Benito Mussolini, and promoting known white nationalists to federal positions within the administration show an alarming trend. Not only that, but the right-wing of American politics has shown a drastic shift towards embracing authoritarianism in recent years as a response to the presidency of Barack Obama.
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Barack Obama is still in office as the US President.
Barack Obama is Protestant