This is a fundamental cultural difference between official American dogma and German everyday word usage.
You might take the stance that in German conversation people despise profanities as much as Americans do. If you avoid the same type of words in German you will not cause much consternation. Politeness is really based on largely the same contexts that those words describe: sexual, bodily functions, race or religion might be avoided (altogether) to stay polite. One example list which also contains a lot of very mild expressions and examples that not many German speakers might find really offensive at all is German Words to Avoid: A Special Slang Glossary (take enough grains of salt when reading it).
But if you use those types of words in German, it will usually not be that much of a concern in German speaking countries.
Let's take a look at a very frequent example: Scheiße
The Cambridge dictionary lists all translations for this word and phrases containing it as "offensive", which probably means: very strong word, do not use if you can't handle the magical power that comes with it.
If we look up Scheiße in German dictionaries like Duden or DWDS, we see just a factual explanation of the meaining and maybe the attribute "derb" (~crass, coarse, crude etc. – but not rude).
If you look at George Carlins "Seven dirty words" there were and are feeble attempts to establish such a code on German airwaves as well. It didn't succeed. When on American public TV such a word is beeped out, you will hear German hosts reprimand the speaker of such words with "Na, aber! Wir sind hier…" or the audience making a Hohoho-like noise. Most of the time: that's it.
Looking for words to avoid in German you will find only tips for self presentation/business settings. The equivalent for "dirty words" or schmutzige Wörter are mostly those vulgar or kinky words used to spice up life between the sheets.
One reason for all these subtle and not so subtle differences start to be entrenched on a very fundamental level and quite early on.
As a form of offensive behaviour and verbal aggression, the use of vulgar language is also a subject of educational consideration.
In German-language parent guides, the understanding of the fascination with children exerted by swear words and "strong language" prevails as well as the need to vent pent-up frustration and the conviction that children benefit if they occasionally cross borders.
In English-speaking countries, however, profanity (= vulgar expression), swearing and cursing (= swearing) as well as name-calling (= insulting) are regarded as expressions of a lack of respect for one's fellow human beings and thus as serious behavioural problems for which various countermeasures are proposed in the relevant guidebook literature.
Coming back to the example chosen you will hear very often little children learning the rules to correct grown-ups they overheard violating those rules they were just taught with: "Scheiße sagt man nicht!" Thereby repeating the offensive act. And without much success for altering the behaviour of the adult, usually.
Using Vulgärsprache does not carry such a drastic social punishment in German. But it can mark you as quite low class.
To summarise: if you want to be really polite in German conversation, just follow the English rules you already know. But don't worry as much as to censor yourself and do not be overly surprised to hear words that Americans might feel are hyper-offensive in normal speech.
Of course, one constant remains the same over time. Don't mention the war! Or, more seriously: Beware of Nazi Words. There are some taboos to better observe. It's not so easy to offend a German by using just a word ('This is X'). But if directing such a word at a person ('You are X') it is easily perceived as offensive.