@CorvusWitchcraft
Among the peasantfolk, same sex marriage is widely accepted and legitimate, tho your parents might be pissed if you’re the only child and don’t have grandkids.
If you romance Hugo in a same sex relationship, Hugo barely gives two flying fucks about tradition and things nobles are meant to care about, like succession. Caring about bloodlines is the mark of an uneducated person, anyway, and all those practices are outdated and irrarional (I think that’s what he’d think) So you won’t have to worry about the Binding, or political pressures around the Binding. You’ll have a lot of other shit to worry about tho, hehehehe.
Lorienne is from Ceton, an Eastern province and she’s the Duchess, I suppose, so about equivalent to Hugo in rank. The East is more liberal than the West, where the player character is from (Westerners often think Easterners are libertines) about matters of succession, marriage, children, etc. Eastern Houses typically allow for eldest child to succeed regardless of gender, and Lorienne has never been pressured to undergo the Binding. Eastern Houses are more open to things like the Binding of Lineage, as per below.
That being said, Lorienne’s House has big money problems. You’ll need to worry about wealth a lot more than gender.
Adoptive magic exists, and it’s called the Binding of Lineage. It allows you to essentially imprint on someone else part or (even) all of your, uh, genetics. But the Binding of Lineage is typically only used in situations of last resort, and kids adopted through this Binding are not usually considered as legit as true born kids. Some Houses accept it, some do not. It’s a bit of a grey area. In fact, the Binding of Lineage was created by Celestial priests to facilitate organ transplants and was first used as medical magic before being used as adoptive magic. An adopted kid by binding faces challenges from cousins, makes succession messier, and you don’t want to use it if things are touch and go politically. But Houses terrified of going extinct and dying out will resort to anything, and Houses have been revived by a binding adoption of a particularly talented child marked, as they say, by the stars for greatness.
And as for Derik, the Crown Prince…
I have no clue
I know the least about Derik right now, and his original backstory that I have planned might not hold by the time I write him.
I feel like Derik would probably pose challenges if you’re pursuing a same sex relationship
But idk. I’ll see.
You can’t spoil ur readers if you don’t bother planning things that can be spoiled 
ALSO if you’re playing a hardcore peasant or Phoenix route, you might not be able to date any of the nobility at all. Some RO’s will be your enemies if you take particular paths. Every RO is from a different background and faction. If you were, say, a supporter of peasant rights and reducing noble power, I imagine you probs won’t have much luck getting a noble to date you…