By the way Secheral you don't have any engineering or research actions yet, you first need to modernize.
EDIT: hoo boy that was difficult to put together.
Homosexuality in both Shinto/Buddhist Japan and Norse/Reformed Norse Countries has some very weird connections and connotations with it. And both are very far removed from common Christian ones.
Japan actually had offically accepted homosexuality especially among priests and samurai. This were mostly pederastic in nature but were usually with consent from both parties. These Brotherhood contracts were monogamic relationships (akin to marriages) for the duration of the training of the minor.
Apparently from there on out Homosexuality slowly snuck into the Middle Class and later into prostitution via kabuki actors.
Interestingly with the Meiji Restoration and Westernization of Japan they did an about face introduced laws against homosexuality (i would assume in all probability due to western insistence) which they dropped 7 years later and since then Homosexuality and LGBT in general is in a weird vacuum in Japan. Basically people know its there, but they don't want to deal with it. And not in a disgusted "this is immoral" way but more along the lines of "Not my business do what you want and dont bother me with it" way.
I would assume that our Alternative Japan would keep its open view towards homosexuality and LGBT in general since no Meiji Restoration ever happened. Along those lines Homosexuality would still be highly ritualistic but going from the seeping through to the middle class i would assume that by now it would have permeated both genders and all social classes. Alternatively it could still be restriced to be a male only practice.
Female Homosexuality doesn't seem to exist at all if one looks at OTL Japan.
Meanwhile Norse isn't as clear-cut either. Divine Figures and Heroes were completely okay to be gay (look at Odin, Loki, Freyr, Sirgurdr and so forth) however what really is frowned upon is to be the LESSER party in such a relationship and to not fulfill ones reproductive duties. This stems mostly from a rather thin population of people and the pastoral lifestyle in Scandinavia.
The Lesser part seems to stem from the fact that one would cease to be self-reliant, would submit and give up some kind of power to the other partner in a homosexual relationship. Female Relationships are not mentioned in the Sagas at all so there is room for speculation there.
Overall however its basically along the lines of "Make some kids, then its okay as long as you keep it quiet." I would assume coming out in Norse Society would be dangerous not for oneself but rather for the partner, mostly thanks to how insults and holmgang works.
By coming out you admit to being in a gay relationship now someone who has a beef with you calls you out as being the lesser partner. Since that would cause Social Ostracism you of course challenge him to a duel. But with that you are in lose-lose situation. If you win, you aren't the lesser partner but by necessity your lover is and thus he is ostracized. If you lose you are the lesser partner and you are ostracized.
In our game i have developed the entire thing to the point where its basically: "reproduce, then it doesn't matter" in most of the world, with gays simply keeping the relationships quiet, while i took the Freedom with Irish Canada to make it more liberal, thanks to a stronger following of Freyr/Freya there, both being gods of Fertility making it in all probability also more liberal in that regard.
As for the various other followers mentioned. Since we don't know how a reformed Norse Faith would look like, i would assume that a polytheistic faith has simply people who follow one god more than the others.
Thus over time more or less Sects and Followings arose.
In our case there are these major sects in Norse Faith:
Odinists - the traditional bend of OTL Asatru and general Old Norse Paganism. Odin as the Central God Figure. I give it a more conservative bend more akin to Italian Catholicism in OTL.
Tyrians - Followers of Tyr. Germanic Paganism and to some Degree Norse Paganism originally worshipped Tyr as the Main God until he was slowly put aside in favour of Odin. With a return of Norse Faith it made internally sense for me that the Religious Warzones of Europe would adopt a more militaristic bend, and turn towards Tyr as a God of Justice and War, since conversion would play a big role, oaths sworn would be especially important and thus Tyr would take a more primary role.
Thorists/Thorians (can't decide on a name here) - arch-conservatives. Thor while being a God of War has also always been the archetypical Farmer God. Since he was bringing storms and thus rain he was often prayed to by farmers. Assuming that the Norse Faith had reformed it would need to allow for mroe than just warriors to go to Valhalla (after all who wants to belong to a faith where he is automatically condemned to Hell if hes not a warrior). Since i read somewhere ages ago something about Thor taking up hard-working people in his hall (and his wife hard-working women in hers), it would make internally sense for Colonists and Farmers to take up predominantly Thor Worship. Of course Thor being the manliest of manly gods, and the very communal nature of Norse Culture and that probably being doubly true if we assume colonists we can assume that Thor Worshippers would be arch-conservative people in general outlook.
Freyans - liberal. A predominant Sect mostly in Irish Canada. Since both Freyr and Freya are gods of fertility they too are farmer and in extension colonist gods. But since Freyr and Frey are also gods of fertility in the more reproductive way it would make sense that those sects would be far more liberal than the Thorians.
Potential other Sects:
Njordans - Njord being the God of the Sea might be especially interesting for Fishermen and Seafaring Nations. OTL his place was mostly taken by Odin and Thor since one was responsible for storms and the other for fate it seemed more prudent to sacrifice to them rather than a mere Sea God.
Resurrectionists - Probably important in Areas converted from Christianity, Especially Spain. Namely worshippers of Baldr. Baldr was actually just a very minor God in Norse Mythology until Christian Influence made him become the equivalent to Jesus. It would make sense for him to show up in areas where abrahamic faiths were strong before.
Hellians - Worshippers of Hel. Similiar to the strong Death Cult in Mexico it would make sense for some countries to have a stronger bend towards the worship of the Goddess of Death, which before Christian Influence made her utterly evil was considered a relatively benign and fair goddess.
Anyway if you have suggestions to the above or want to discuss it feel free to do so, if its good i might take it over. Especially the names need improving in many places