Hitler passed a gun control act in 1938 which attached a "sporting purpose" test to gun purchases; this law was basically copied into the GCA of 1968 in America. Also, Hitler actually did prohibit Jews from owning guns; any Jew found with a gun was summarily executed.
But, it is true that general gun registration in Germany began under the Weimar Republic and Hitler only made wide use of these lists when he went after the Jews.
As with all such things, reality is far more complex than the soundbite I tried to give.
All guns were completely outlawed in 1919 as a result of the Treaty of Versailles. (Due to fears that a disarmed government would be too vulnerable to an armed public, so they disarmed the public.)
In 1928, the laws were liberalized to allow guns, but with a very strict registration regime. The 1938 law you referenced actually liberalized this strict regime, making it easier to own guns, especially long guns. Government workers and party members (and hunters, your "sporting use" part) were exempt from getting the gun permit.
Jews, of course, were prohibited from owning guns, a task made far easier by the 1928 law.
Honestly, I think making the point that Hitler's crimes were made easier by gun control from a previous administration makes our argument easier. We don't have to claim our opponents are Hitler, just that things like registration make crimes like his easier.