What's a word to describe topics that would be impolite to talk about?

I think that you are referring to behaviours that are considered normal or usual within a community. Taboo probably has a too strong connotation.

I think custom or consuetude may fit the context:

• a usual or habitual practice; typical mode of behaviour

• (Sociology) the long-established habits or traditions of a society collectively;

  • convention: custom dictates good manners.

(TFD)

You've already had unmentionable in the comments. Consider also unspoken. If something is in the background of a conversation but not directly mentioned because it's a too sensitive topic then you might even call it the elephant in the room.

Some topics are considered unsuitable for conversation - traditional dinner party etiquette says to avoid religion and politics. Others add money, bodily functions and body odours - the phrase for this is that such topics are not to be discussed in polite conversation or are not for polite company.

If we confine the question to the topics you use as examples, then polite or taboo may be suitable labels. However, if you extend the range of conversation to topics such as corporate profit margins, The President's home phone number, how much money you made last year, or the combination to your home safe, you probably would classify these as private, prohibited, or privileged topics.

This could also be referred to, variously, as examples of a social indiscretion, impropriety, or gaffe

indiscretion noun:

1: lack of discretion: imprudence

2 a: something (as an act or remark) marked by lack of discretion

b: an act at variance with the accepted morality of a society see, Merriam-Webster indiscretion

impropriety noun: plural noun: improprieties

a failure to observe standards or show due honesty or modesty; improper language, behavior, or character. See, Google impropriety

gaffe noun:

1: a social or diplomatic blunder

2: a noticeable mistake. see, Merriam-Webster gaffe

You don't want to make a "faux pas". Which according to Wikipedia:

... is a socially awkward or tactless act, especially one that violates accepted social norms, standard customs, or the rules of etiquette.

This may be a little too specific, but my favourite phrase for the subject that everyone is aware of but no-one dares talk about, is "elephant in the room."

You could call them private matters, since they're usually discussed only with those concerned instead of just anyone.

Uncouth is a word I often use to describe how I feel discussing money owed to me by friends or family. Like I feel “tacky” “trashy” or the opposite of classy, asking “hey when are you going to be able to pay me back for that $___ (which is usually in the hundreds of dollars, not just $20 here or there) I lent you __ months ago?” Does anyone else feel this way discussing money in general?