Jewish law and thought covers all aspects of life and that means nothing is beyond the purview of Talmudic and rabbinic discussion. With the primary theme of masechet Sotah being that of marital infidelity we should not be surprised to find rabbinic discussion focusing on exactly at what point is one considered to have engaged in an illicit sexual act.
In order to declare a woman as a Sotah she must be caught alone with a man she has been warned to stay away from. The Gemara asks for how long must they be alone? What follows is no less than ten responses; each in Rav Yochanan's words, "defining the duration [of coition] from his own experience". The Gemara continues with a profound insight explaining that adultery is much more than a sin of sexual lust. Rather it often is the result of arrogance - of thinking one can basically do what one wants. "Rav Chiyya bar Abba said in the name of Rav Yochanan: Every man in whom is haughtiness of spirit in the end will stumble through a married woman" (Sotah 4b). Those full of arrogance know of no limits, thinking they are the centre of the universe. No wonder "Rav Chisda and some say it was Mar 'Ukba said: Every man in whom is haughtiness of spirit, the Holy One, blessed be He, declares, I and he cannot both dwell in the world (Sotah 5a).
Yet linking the discussion of adultery and arrogance is one concerning the mitzva of netilat yadaim, washing one's hands before a meal. "Rav Zreikah said in the name of Rabbi Elazar: whoever belittles the washing of the hands will be uprooted from this world" (Sotah 4b).
This teaching is difficult to comprehend - what exactly is so terrible about not washing one's hands? Even more difficult is the teaching equating neglect to wash one's hand before a meal to adultery itself. "Whoever eats bread without washing one's hands it is as if they had relations with a harlot" (Sotah 4b). The Gemara actually brings scriptural support for such a position! "'For on account of a harlot [a man is brought to] a loaf of bread" (Mishlei 6:26). The 3rd century Babylonian sage Rava, noting that the verse begins first with a harlot and only afterwards discusses bread. 'reverses" the teaching so that "whoever has relations with a harlot [in the end] will be [forced to] beg for a loaf of bread". Netilat yadim may be a mitzva but can we really compare this rabbinic mitzva to adultery?
Before we even discuss the mitzva aspect of washing there is the aspect of health. Our Sages note that one must be more careful regarding potential danger than a potential Torah prohibition (Chulin 10a). Before washing of hands became mandatory for hospital workers thousands perhaps millions died before their time - there was little awareness of how [easily] germs could be transferred. So one who does not wash may literally be "uprooting" themselves from the world.
And it is not uncommon for one who has an affair to be thrown out of the house and see their life go on a downward spiral so that one who "has relations with a harlot [in the end] will be [forced to] beg for a loaf of bread." Sometimes one mistake can really ruin many lives.
But how might we explain the view that neglecting netilat yadaim is akin to an act of adultery? We might start by noting that Judaism sees holiness specifically in the area of food and sexuality, with the phrase and "you shall be holy" appearing by both sets of laws (see Vayikra 11:44 and Rashi, 19:2). Maimonides details the laws of "forbidden relations and forbidden foods" in Sefer Kedusha, the book of holiness.
While the severity of the prohibitions are very different - sexual immorality may in theory be a capital offence whereas forbidden foods are generally "just" a plain prohibition - conceptually they are most similar; we attain holiness by sanctifying the physical. Both eating and conjugal relations are aspects we share with animals. But unlike animals we can control our desires and passion. Washing before we eat is a small indicator that we don't just grab and eat, we first prepare and bless and only then can we eat. Similarly what defines a harlot is the sexual act done without the sanctification of marriage. Both eating and conjugal relations are meant to be mitzvoth - but only if proper preparations are made.
 The Talmud queries as to how one of these views could be that of Ben-Azzai who "did not marry". To this the Talmud gives three responses (Sotah 4b).
 In fact, the Talmud says that the "first water" [before we eat] is a mitzva and the later water [after we eat] is an obligation" making its importance even less so. Here again is another example of mazel in mitzvoth; people are much more careful about washing before eating but few are careful to do mayim achronim.
 It is important to note that the work keeilu, akin, does not mean to fully equate. It's as if but is not the exactly the same.