In particular when ham-sters are using the VHF or UHF bands and talking to each other through repeaters(as well as local radio nets). But also what about DXing? Do FCC obscenity regulations apply equally to all amateur radio bands?
The amateur radio community is largely self regulated. So violations of amateur radio rules are rarely directly directly observed by the FCC. Usually it requires complaints from the amateur radio community for the FCC to initiate action. Typically, for FCC to make a direct observation of a violation, it would have to be a repeat violation, very flagrant, or so severe as to interfere with other radio services. Typically, amateurs try peer pressure to fix violations before attempting to get FCC to start enforcement actions. ARRL recently published an article about this.
The rules governing amateur radio are actually a bit tighter than for broadcast radio, as amateur radio transmissions are suppose to be family friendly. However, enforcement of them is more lax than with commercial radio, and penalties are at least initially much lower. The amateur community would probably complain about commercial use of amateur radio (which is explicitly illegal) before they complained about profanity.
Having said that, there have been cases where amateur radio operators got in trouble with the FCC, usually because other amateur operators complained. The results of such violations eventually result in loss of the amateur license.
Continued transmitting without a license is a serious violation that can result in very large fines and in extreme cases, jail time.
No amateur station shall transmit [...] obscene or indecent words or language
These are not the same regulations that prohibit TV stations from broadcasting obscene or indecent content. However, the above language applies specifically to amateur radio in its entirety.
To my knowledge, the U.S. Code does not explicitly state what is "obscene" or "indecent", but the FCC is responsible for enforcement and has issued some guidance, which is in turn based on legal precedent.
FCC obscenity regulations
no such thing. It's US Code, and the FCC is only the enforcing organ.
So, the FCC themselves say they enforce things on a "we know when we see it" basis, which, for me not coming from a US background, is a pretty strange way of regulating things fairly, since that basically means there's mostly case law, ie. previous decisions to base one's rights on. ugh; especially, ugh, because that's a "random range of decisions" applied to the constitutional right to free speech (and there's high-publicity cases about exactly that).
However, the law in question: 18 US Code §1464 says¹ in verbatim:
Whoever utters any obscene, indecent, or profane language by means of radio communication shall be fined under this title or imprisoned not more than two years, or both.
So, that doesn't deal with ham radio any different than with ABC news. Now, again, this is all case-law based, so only the judge in your case will be the authority to tell you what applies and what doesn't.
This is an extreme case of "you'll have a bad time if you solely rely on free online legal advice", so file a complaint if you want to, and if a complaint is filed against you, it's probably time to get a lawyer. Good luck!
Notice how it's not even a very well-stated law: "radio communication" could be the best-encrypted exchange between you and your lover, with very personal, very indecent, very obscene content. Only the title of that paragraph, "Broadcasting obscene language" lets the reader in on the original intent to limit this to broadcasting, which again is a broad term – technically, all ham radio communications is broadcast. Morally, the point of the law was to restrict free speech in a way that protects e.g. minors from indecency that they have little choice in receiving, so little sense in regulating ham radio as strictly as nationwide radio syndication.