Most English speakers will take slightly different meanings from each sentence. "He gets up at eight every morning" says to me that he has done that in the past, he still does it, and he will continue to do it; it says to me that it's a constant thing with him. "He is getting up at eight every morning" sounds more temporary to me; he is currently getting up at eight, but he didn't in the past, and he might not in the future.
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