I think you already know that お- and ご- prefixes are often added to the beginning of nouns to make them more respectful. However, sometimes this is not always the case. I am by no means an expert on this topic, but I can regurgitate some information I have read before.
美化語 is literally the "beautification" of words. By adding honorific prefixes to the beginning of nouns, people are able to make their words sound more refined. Sometimes, this is for politeness.
Although this is not a definite rule, お- is typically added to the beginning of words of Japanese origin as well as 和製語【わせいご】 (Chinese/Sino-Japanese created in Japan). It also, but less commonly, attaches to the beginning of words of foreign origin (like おビール).
The ご- prefix is typically attached to Sino-Japanese words that do not use お. Since these rules are pretty loose, you would have to get used to which words are used with which prefixes on an individual basis.
Prefixes like み-, おみ-, and おんみ- also fall under 美化語 and are generally used for things with holy or imperial importance. （like 御子【みこ】）
Some 美化語 comes from feminine speech. You may have noticed that women are more prone to adding honorific prefixes before nouns, which makes them sound more refined or polite. Some 美化語 that originate from feminine speech but are now widely used are: おかず、おつけ、お腹、おなら.
In more respectful settings, however, attaching honorific prefixes often becomes the norm and is no longer restricted by gender.
When the Prefixes are Necessary
Some words have evolved so that they are never used without honorific prefixes. One example of this is the word お化け, which means "ghost" or "apparition". The word 化け has completely different meanings and is by no means interchangeable with お化け.
These words range from "the prefix is always necessary" to "the prefix is usually used, but sometimes omitted". For example, お湯 is usually used with お-, but can sometimes be seen without the honorific. お世辞, however, is always used with its honorific prefix. Your example, お金【かね】, would fall into the "usually" category.
Changes in Pronunciation and Meaning
Sometimes, the meaning and even the pronunciation of words will change when honorific prefixes are attached. Here are some examples:
釣り(fishing)→お釣り(change e.g. for a purchase)
This may not be the most in-depth explanation of 美化語, but I hope it explains that honorific prefixes are more than just for being polite. What used to be feminine language is now widely used by speakers of any gender. Other words can only be used with honorific prefixes, lest they sound unnatural. Some even change in meaning, pronunciation, or both.
お金 is part of this. Although I am not 100% sure, I am assuming that it is part of the "usually used with honorific prefixes" category. I have seen it alone as just かね in some books.
Neutral words with honorific prefixes
honorific 「お」or「ご」 as a necessary prefix