Spiritual Unity in Judaism is defined by Toisfos (the second great commentary on the Talmud, after Rashi) in Gemora Chulin (135a.) Toisfos explains that the Jewish people are mentioned in the singular because they are all obligated in mitzvos (commandments.)
This idea underlies a crucial concept in Torah, leading to an understanding of the purpose of the Jewish People in the world.
Through this we can comprehend the Jewish view of Utopia with all of us living in Eretz Yisroel (Israel) as a people of the book where literally every step we take is mandated by a Torah mitzvah. As we say in the Shma; kimei hashamayim al haaretz – like the days of the Heavens on the earth (Devarim 11:21.)
The Torah starts with the letter Beis (see Husband and Wife Relationship.) Beis has the numerical equivalent of 2. In this lies the very essence of the physical universe.
The universe is founded in the division of opposites. All physical growth can only take place from the conflict of opposites, night and day, hot and cold, full and empty, male and female.
In Hebrew the words for battle (riv) and increase (rav) have the same base letters, perhaps for this very reason. There can be no growth without battle.
There are 4 levels of battle (heard in a shiur by Rabbi David Lapin):
On the contrary at the highest level the Chazal (Cahchamim zichronam livracha - the sages of blessed memory) say ailu veailu divrei Elokim chaim hein (these and these are the words of the Living God – Eruvin 13b, Gittin 6b.)
Meaning that even if two valid opinions are diametrically opposed, they are both true because they represent different aspects of Hashem’s (God's) Torah, just as colour from a prism represents different aspects of white light. (As a corollary, for practical observance, we generally only take one opinion as Halacha - law.)
This is the ultimate form of spiritual unity in Judaism.
The purpose of a Jew as an individual and of the Jewish people as a whole and in fact the physical universe, is to turn this apparent duality into one by revealing the Essence of creation through spiritual unity.
This leading to the ultimate realisation of Hashem Echad uShmo Echad (Zecharia 14:9) (Hashem is One and His Name – ie His attributes, realised as interactions with the universe - are One.)
In the second paragraph of Shma, which is about the adopting of the yoke of mitzvos, we are referred to in the plural because, indeed, when it comes to the acceptance of mitzvos we all have to do it on an individual level. This, in fact is the catalyst for converting the duality into one whole.
The Jewish People living in the land of Israel and following Hashem’s Torah in every aspect of their lives, is the epitome of the battle of opposites being one in spiritual unity.
Every individual with their own specific needs, wants, strengths, weaknesses, abilities and talents focused on the fulfilment of the Will of Hashem is the ultimate realisation of Hashem in this world and the purpose of Creation. This is spiritual unity in Judaism.