In Texas, death certificates are available free of charge to anyone with access to the internet at familysearch.org up to 1976, including cause of death. Every state makes its own rules about obtaining state registered deaths. Ive ordered in records for clients from just about every US state, and you would be amazed what I can find on just about any American in a short period of time. PA recently became much more open. It used to be I had to have clients order their own certificates from there, even ones like death certificates over 100 years old.
I think it is important to recognize the difference between posting something that was (also?) on a death certificate and obtaining an actual certified copy of a birth/death certificate. I am not a lawyer, but I am quite sure that is it not illegal to post a cause of death for a person in any state of the USA. Rude, inconsiderate, etc perhaps, but not illegal. Think about it, do you know of any state that doesnt have news reports of murdered people or traffic accidents etc?? even waiting until after notification of next of kin is a courtesy extended by any media outlet that doesnt want to be cut out of the loop of police notices but not technically a legal requirement I think.
I operate under a "living first" method, where if a living person has a request that isnt complelely unreasonable, I usually follow it. If I think a certain record is quite likely to cause hurt feelings/upset someone I omit it. If I find something iffy when researching for a client, I inform them what I found and offer to leave it out of the report if they dont want it included.
And I am quite sure that Geni has (had until now?) no policy against peoples dead children being listed as public profiles because I know of one where the a parent did not consent to a profile or it being public and there was nothing to be done about it. Again, rude, inconsiderate, and not what I personally would do (I would never, ever even think about adding a death certificate for example of a sibling of a Geni user!) but not technically illegal or against the rules. Courtesy and manners are a different thing than law (or website policy)