Was possession of weapons prohibited, encouraged, allowed to members of some organizations, or what?
As @Nathan Cooper indicated, under Hitler, most of the civil weapons legislation was not actually Hitler's - he inherited strong gun control laws from Weimar Republic (aside from total prohibition for the Jews since 1938).
However, the laws were written in a way that allowed pretty much unlimited restrictions and limitations by people in power, within the framework of that legislation:
- Guns were required to have serial numbers
- anybody owning one without a serial number had to have one stamped on it.
- Permitting was mostly left up to the police.
- Permits were only given to people of "undoubted reliability" who demonstrated a "need" for a gun (Hello from New York City).
Note the laxensess of definitions. The last bullet point was such that pretty much anyone you didn't want to have a gun wouldn't have one.
A very detailed discussion is in the second half of the Straight Dope article here (the first half was mostly devoted to debunking an infamous Hitler's gun control "quote").
Germany had very tough gun laws after WWI, which were gradually relaxed during the Weimar Republic and the Nazi regime. I'll paraphrase German Wikipedia:
Immediately after WWI, private gun ownership was outlawed, however this was impossible to enforce because guns were not registered. Especially post Freikorps right wing militias (Schwarze Reichswehr) were well armed
In 1928, Germany got its first unified gun law. Private gun ownership was allowed. However, prospective buyers had to prove their "reliability" and an actual need for the weapon. Weapon owners needed a Waffenbesitzkarte and a Waffenschein (a license to be carried on the person)
After 1933, the Nazis used the existing laws to harass Jews and political enemies: the police would withdraw the permit and use this as a pretext to search someones premises for weapons. This was targeted widely at Jews (in '33, Berlin's police chief withdrew all weapons permits from Jews) but also at other political enemies.
Later, the Nazis would control who gets a gun: gun laws were relaxed for party members (a license was no longer necessary to carry a handgun, starting at certain ranks within NSDAP, SA, SS or Hitler Youth among others), while "Gypsies" and other were banned from gun ownership. Jews were excluded from gun or ammunition manufacture and sale. at the same time, the restrictions on longarm ownership were relaxed, permits were only required for handguns. A specific goal of this law was Wehrhaftmachung des Deutschen Volkes, to ready Germans for war.
Later in 1938, after the November pogroms, a bylaw specifically forbade Jews guns or any other form of weapon ownership
Another element of gun politics where gun clubs - I have not found much information, but in 1936 all gun clubs where gathered under the roof of the *Deutscher Schützenverband," in 1938 they were put under control of the SA. Contemporary historiography looks more closely at the politics of the individual clubs (many of which, especially the more sport oriented ones, submitted quite willingly). It appears however the politics re. gun clubs was also motivated militarily - train Germans to shoot.
So you certainly can say that in the 20ties, Germany increased gun rights - from none at all to legal gun ownership, based on permits. To answer the the question if gun ownership in certain groups where "prohibited, encouraged, allowed", I think we can identify three broad trends.
- allowed, maybe encouraged: handgun ownership for "reliable" Nazis
- allowed, maybe encouraged: longarm ownership for most Germans, in the hope that a population that practices shooting makes better soldiers. I think the regimes interest in gun clubs could point to "encourage" but this would require more research
- prohibited: potential political opponents, Jews and Gypsies, gun laws and bylaws where also used to harass these groups
I don't know if the Nazi or Hitler ever systematically laid down their thoughts on private gun ownership, I don't think there were coherent pro- or anti-gun views in place. Rather it was general Nazi-politics that also shaped gun policies:
- Antisemitism, in that Jews where excluded from gun cliubs, gun ownership and gun making
- disarming political opponents
- militarization of society that called for broad training with and accessibility of longarms
- Nazis wanted the tools to terrorize their opponents, or protect themselves
- (mostly) the (usually local) police that used the laws passed on a federal level to harrass Jews, Gypsies