The European English and American English versions were localized from scratch each separately, that much I can confirm.
About the Japanese version, at least a sumo event became something else (a golf minigame) in the common build that was used later to create all the Western localizations. There were other differences. It's a very interesting subject in fact.
NO SAME-SEX FEATURE OF ANY SORT EXISTED IN ANY OF THE VERSIONS OF THIS GAME (beyond creating a Mii with gender set to something and physical features set to something else, something possible in the Mii creation tool in any version/Nintendo games in general).
The jist of the story is: Tomodachi Life (aka Tomodachi Collection in Japanese) is actually the 3DS sequel to a Japan-only DS game (that has a partial fan-translation btw -only missing some song lyrics-, check it out!), where you can also import Miis from your Wii to the DS through wireless connection.
Guess what, the Japanese version of the 3DS game had a feature to import Miis from the Japan-only DS game (said feature is no longer available in the localized builds, obviously, since Nintendo couldn't localize the DS one to begin with -a problem with the Volcanoid software-).
There was a serious bug in the import process. A bug that would generate invalid Mii data with the side-effect of randomly pregnant men, and the game crashing and wiping out the entire save data, recognized as invalid/corrupt data.
Nintendo Japan issued a patch to the DS>3DS import feature as well as other fixes, and a press release mentioning this and using the wording "the bug was causing invalid Mii behavior".
Western gaming "journalism" reported this initial incident back when the game wasn't even considered for localization as "Nintendo's filthy xenophobes patched out same-sex mariages/relationships/Mii...". When it was finally localized, finished, with review copies coming out, someone put out a campaign "Nintendo please add in your next Tomodachi game feature X" and then the shitstorm begun, with every single gaming "journalist" spreading lies and talking about a hypothetical non-existent feature that was censored in non-Japanese versions (even Sterling).
Bill Trinnen made the huge mistake of trying to reach out in a human, empathetic and cool way to that asinine SJW community, saying that nothing was censored, those Japanese screenshots were from people creating a Mii with gender set to something and physical features set to something else, and "you can do this in any version".
That information was interpreted as "if you want to do it, do this" and then it was called "offensive", "not making distinction between gender and orientation", "NOT ENOUGH!" and then a flood of threats and insults altogether to Nintendo Treehouse employees.
When the truth (aka someone actually taking the Japanese and English builds and comparing them by himself) begun to filter out gradually among the manufactured misinformation... They spin it as if a localization job is expected to alter fundamentally and add big gameplay changes to a game and account for every political correctness issue ever... or about how this controversy is necessary so that games become the device to implement social commentary or educate kids specifically and forcibly expose them to some beliefs or world views besides their natural education and upbringing.
And the rest is history.
