After having followed the below steps, you will be able to:
-Have spouses of the same gender as yourself
-Bribe storks to bring your gay couple children

You will not, however, be able to:
-Have NPCs dynamically marry non-player characters of the same gender

As extras in the Technical category all the way down, I will also tell you how to:
-Be transgender
-Be two Dwarves in a trenchcoat pretending to be a Troll
-Make others transgender or two Dwarves in a trenchcoat pretending to be a Troll
-Become non-binary
-Acquire a cat girlfriend

As you might have figured out already, we will be editing the save file, and swapping a character's sex. It is simplest to do this to the player character, and create them with the sex you want them to have afterwards, because appearance stays the same when swapping gender.

Now comes the fun part. Navigate to the Soulash 2 save directory, located in "C:\Users\(username)\AppData\Roaming\WizardsOfTheCode\Soulash2\saves", and find the save with the name of the world you and your would be spouse occupies. It is advisable to back the entire world file up in case it is somehow corrupted in the process.
After that find player.sav and open it up, you can use Notepad++, or, if you are really daring, base notepad. On a line beggining with "Humanoid" somewhere around line 15 you should see "Humanoid;(number)||0|(1 or 2)|0". The number after "Humanoid" is the race ID, and the 1 or 2 is the sex of your character, 1 being male and 2 female.
Yep, you know where this is going, swap the 1 for 2 or vice versa and save - this will genderbend your character - then load the save. They will look the same, however. Now you can propose! Yay!

After you earn the heart of the love of your life, you can switch the sex number in the "player.sav" file back. Lo and behold - you are now a gay couple, how queer! Rejoice!

I have attempted to find out how to enable the marriage dialogue for the same sex, but alas, it appears to me to be controlled by something outside the core game in the mod folder. It seems the type of conversation as shown in the "conversations.json", that being ""type": "marry"", dictates what gender can propose, and is established somewhere uneditably.

I was not able to figure out what determines what family someone is a part of. Adding an additional spouse to the player only shows the player as the spouse in the NPC's intel screen, but it only shows the first spouse for the player.

You can use throwaway characters to edit the appearance of you and your spouse. Create the appearance of the character you want on a new world, then open up their "player.sav" according to the instructions of step 2, copy the entire line beginning with "Glyph", and replace the Glyph line of the character you want to edit the appearance of. This works in between races, so you can also have faux interracial marriage (though all of the "hybrids" will be of the same race), and potentially custom glyphs!

It is possible to also change your race in order to propose, and then change back. However, all of the children will be of your spouse's race.

Your spouse can also be edited like this, but you have to find them in "actors.sav". In the file, search for either their first name or surname, or both, but put "|||" in between them instead of a space. The specific character's data has a border of two lines saying "ENTITY:", everything in between them along with the name is the data of the character. Just as was mentioned above, you can replace the line beginning with "Glyph" to change their appearance.

I have also, by accident, found out you can enter your gender as 0, which will make you "undetermined", so enjoy being non-binary!