Opposition wouldn't, in this case, have to be the communists but rather anyone he perceived as a threat to his power.
Some of the opposition he faced was from within his own party. Earlier in the 1920s the NSDAP had been a rather socialist party. They had put out a 25 point plan that stated their goals. Much of it was quite socialist. Not much of it was ever implemented. Over time the party, especially those such as Hitler and other high ranking members of the party, moved more to the right. After gaining power Hitler saw the left leaning members, especially those such as Ernst Roehm, to be a problem. Roehm especially kept pushing for more socialist policies to be implemented (there were other things that annoyed Hitler such as Roehm's street violence in a time where Hitler was trying to soften the view of the party I guess you could say). It got to the stage where Hitler had quite a number of the left leaning faction in the NSDAP, not to mention others in the wider society, including former politicians, assassinated during the Night of the Long Knives in 1934.
The historian Ian Kershaw has written books covering this, such as "Hitler", which is seen as one of the better books on Hitler's life, not to mention numerous interviews and newspaper articles.
The Reichskonkordat was signed in 1933 between Germany and the Vatican, and it detailed the rights of the Church and the German state, and the limits on those rights for both parties. From the beginning, there were violations by Hitler's government. There was continual interference by the State in what the treaty recognized as Church affairs. Violations of the Concordat increased after March of 1937 when the encyclical Mit Brennender Sorge voiced the Vatican's concerns with fascism, especially what it called the "idolatry of the State." In the wake of the encyclical's publication (which was dramatic in itself, having been smuggled into the country and spread by motorcycle couriers so that it could be read from every Catholic church in a single day), the Nazis banned Vatican radio and shut down Catholic newspapers. Catholic youth groups were disbanded in favor of forming Hitler Youth groups. Vatican protests of violations of the Concordat reached into the dozens before WWII began, somewhat obviously falling on deaf ears.