Considering the Pope was sitting in Vatican City, surrounded on all sides by Mussolini's Italy, neutrality might be well-advised.

Actually, it's partly thanks to Mussolini that the Pope got Vatican City in the first place. For centuries, the Popes ruled a country called the Papal States. But Italian unification was a big thing in the 19th century and obviously Rome would have to be the capital of a united Italy. But if Rome was to be the capital of Italy, where would the Pope rule from? This was known as the "Roman Question".

In 1870, the Papal States fell and the Pope declared himself a "prisoner in the Vatican", viewing himself under siege and refusing to recognize the new Italian state. In 1929, Mussolini's government resolved the situation by giving the Pope his own tiny country, Vatican City. As part of the Lateran Treaty, which founded Vatican City, the Pope was obliged to remain neutral in any future wars.

The Lateran Concordat was signed between Italy and the newly created nation of the Vatican City in 1929. Article 24 reads as follows:

In regard to the sovereignty appertaining to it also in international matters, the Holy See declares that it desires to take, and shall take, no part in any temporal rivalries between other States, nor in any international congresses called to settle such matters, save and except in the event of such parties making a mutual appeal to the pacific mission of the Holy See, the latter reserving in any event the right of exercising its moral and spiritual power.

The Vatican City shall, therefore, be invariably and in every event considered as neutral and inviolable territory.

So neutrality in foreign affairs was a treaty obligation.

That doesn't mean that the Pope was "silent" during WWII, as is sometimes alleged. This earlier post of mine covers that question in some depth, but follow-up questions are always encouraged. One addition to that post that should be made is that of Robert Ventresca's book Soldier of Christ: The Life of Pope Pius XII. Finally, there is a book that I can recommend on the subject of Pius XII with no real reservations. It is a true biography, and manages to be free of strong bias either for or against the pontiff. My own arguments on the subject are similar to Ventresca's. I encourage reading his book as well as my post if you are interested in the subject.

Ancillary question - if the Vatican had not been neutral how would that have effected the safety of Catholic communities? Catholics were a large minority in Germany, would their sheer numbers have protected them from the discrimination faced by smaller minorities?