Were concentration camp guards allowed to talk about their work at home?

Camp guards were not permitted to disclose anything that went on in the camps and were held to a secrecy code. There were rules in place also for camp guards about treatment of prisoners and misappropriation of Jewish property and of course we know all about the atrocities that occurred there. In the many interviews I read with former prison guards they mostly felt they were just doing their duty and did not deserve further punishment for what happened in the camps.

You are confusing two different things: extermination camps and concentration camps. There were dozens of Nazi concentration camps, but only six extermination camps. The guards at the extermination camps were a small number of fanatical SS soldiers who were dedicated to carrying out their tasks in the most secretive way possible. Himmler, the boss of these men personally selected them and trained them to be secretive and there were express policies in place that made it a serious offense to be any way discussing extermination procedures or events with anyone, including girlfriends and wives.

No, they weren't. Even concentration camp inmates who were incarcerated temporarily were required to sign a paper that they would never tell anybody about what they saw in the camp.

This information was secret for many reasons. Not only to hide the Holocaust, but to hide other abuses as well (of non-Jewish prisoners), to hide information on who were the prisoners (there could be important figures inside), on the ethnic composition of prisoners, on the jobs the prisoners were occupied with (this was war secret), on the medical experiments performed and so on.

As noted by Tyler Durden, you need to differentiate between concentration camps and extermination camps. So far as the former were concerned, they were not only well known but needed to be well known. Prisons can hardly serve as effective deterrents if their existence is kept a secret! According to Robert Gellately, the Gestapo never had more than about 32,000 employees. Since there were approximately 60,000,000 people in Germany alone, they were only ever going to be effective if people knew precisely what would happen were they to be arrested.

Such was not the case when it came to extermination camps, the existence of which needed to be kept secret for more than one reason. For a start, it was imperative that victims not know where they were going and what was going to happen to them when they got there. The SS went to great lengths to preserve the mystery around these places, telling people to bring luggage with them, changes of clothes, cutlery and a small amount of money - and even, in the case of Jews from Iannina in Greece, purchasing tickets.

Secondly, the Nazis also wanted to ensure that the outside world would know as little as possible about the purpose of these installations. Battling against the Russians on the Eastern Front, the last thing they wanted their enemies to know was that being captured would involve being subsequently murdered. To win this war, the Nazis needed the Russians to surrender. When word got out about the wholesale murder to Soviet POWs (some 2,000,000 - approximately), the Russians knew that it was in their best interests to die fighting.

Finally - and most germane to your question - the Nazis did not want their general population to know. With all that was going on (rationing, power shortages, allied bombing), they counted desperately on the continued support of their own population. It is one thing for people to look the other way when they see people being persecuted, even violently; it is quite another to know that entire communities of people are being murdered through an impersonal, industrial process.

That said, while guards were under strict orders not to speak about what they saw and what they did, people always speak about what they see and what they do. When given time away from work (which was every so often), people not only spoke about what they had seen, they did so in great detail. Some guards had personal photo albums that related to the times they had spent in individual facilities - and, of course, the same thing goes for shooters. (Most of the so-called "Einsatzgruppen" photos were taken by perpetrators, and many were sent home to their families by post).

I don't personally know of any instances of people being punished for revealing information to their families and friends, although that may have happened. They certainly weren't supposed to.

Let' just say that it was highly discouraged.

First, unlike "regular" prisons, guards at concentration camps did not go home every day because it was a quasi military function. Even when "off duty," they would be either in or near the camp most days, getting a few weeks of "leave" each year.

Second, many were too shocked by the horrors of what they saw to discuss it with their families. One "exterminator" (not guard) on the eastern front reportedly wrote in his diary, "How I can tell my parents I kill babies every day?"

Third, their work gave them a first hand insight about what happened to "dissidents" or "undesirables" or just people who talked too much. No one would want to go from being a guard to being an inmate at one of these camps.