Nazis were huge fans of statues - they put up as many as they can. The only instance I'm aware of that they tore them down was during the occupation of Paris, but that was more to commandeer iron to manufacture ammunition supplies.
Guns were already a controlled commodity in Germany, even during the Kaiser days. German civilians never really had a high rate of gun ownership to begin with, and that remained true through the Weimar era, through the Nazis, and through to this very day. I can't emphasise enough: we're the onyl country who really do that to begin with. Even Switzerland takes gun safety more seriously than we do.
Well known Nazi slogan: "Kinder, Kirche, Kuche" - their instructions to all women living under their regime, have kids, go to church, and cook. German Protestantism was spearheaded by Nazi government, not surpressed. It was very near the top of their agenda: put German church back into German culture. They were obsessed with it.
Health care was a Weimar thing, the Nazis just wanted to cut the costs of the national healthcare by kicking the Jews out of it.
And Volkswagen, BMW, Mercedes, Hugo Boss, etc, were not supressed under the Nazis - they had the time of their lives.
TL;DR: yes, it DOES sound like the modern Democrats - because you're not talking about Nazi policies, you're talking about modern Democrat policies and saying it was Nazis. You are a liar. The Nazis did not have these positions.