Many people would never dream of going to synagogue without showering or brushing teeth. But on Yom Kippur, many Jews choose to abstain from these and a few other hygiene practices.
Yom Kippur is a fast day — Jews, with some exceptions, do not eat or drink. Since it’s easy to swallow a bit of water or toothpaste when brushing one’s teeth, many skip that too. Moreover, Jews are discouraged from washing or showering on Yom Kippur, since it’s a day to focus on internal cleanliness — not external appearance.
For similar reasons, using creams or lotions is also frowned upon as they are seen as pleasurable physical acts that contradict the fasting and asceticism of Yom Kippur. Some rabbis hold that spray-on deodorants are acceptable if absolutely necessary, but that gels and creams should be avoided regardless.
The point of all these practices is not to promote uncleanliness, but to enable those observing the holiday to stay focused on something greater than their personal comfort and convenience.