A member of your neighbors' family died, and it was critical that the burial take place very quickly. You asked why and learned that the family's religion does not allow embalming or other procedures to take place. What religion does your neighbor adhere to?

The answer to the question: What religion does your neighbor adhere to, would be: Islam.

Explanation:

Islam is a very old belief system and faith that has been present in the world for centuries and is very much alive today. It is the belief system of almost all Middle-Eastern countries, and at the very least, those of Arab ascent. In the case of religious law, and how people should proceed according to the preachings of Islam, in all matters of life, including death, Muslims adhere to two sources: The Quran and the Sharia. The Sharia is precisely the code of rules that are given to all believers of Islam so they can perform their daily activities in accordance with the teachings of Allah, given to them through their Prophet, Muhammad.

In the case of burials, the Sharia states that a body must be buried within the following 24 hours of death, with only a few exceptions. The body must be buried, not cremated, and it must be done after a simple ritual of bathing and shrouding. These are the characteristics described in the context of the question, and therefore, this is why Islam is the right answer.