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So, Heidegger was a Nazi for a while. That much is clear.
What's not so clear is how well Heidegger understood Nazism. He joined the Party in 1933, and although he never actually left it, he stopped actively participating in 1934. Some of his work was even banned by the Nazis at this point (source). Some people think Heidegger was a committed Nazi; others think he didn't really understand the political reality and just wanted to be a part of whatever was going on at the time.
Scholars can't agree on this issue, and they also can't agree on whether they think Nazi ideology or anti-Semitism compromises Heidegger's philosophy. This is a big issue, since Heidegger has had an enormous influence on 20th- and 21st-century continental philosophy (phenomenology, hermeneutics, deconstruction, and existentialism) as well as on contemporary theology, psychology, critical theory, and political theory.
In fact, Heidegger might be the most influential thinker of the past century, so if his philosophy is tainted, then it's not unreasonable to question whether the schools of thought he influenced are likewise marked tainted. The jury's out—way out—on this, but it's something anyone studying Heidegger should be aware of.