Let me illustrate it this way. What is the difference between a sexualized/objectified character, and a sex-positive character?
The answer is agency.
Is the sex on their terms? Are they an active participant? Do they make choices? Are their wants and needs, considered important? Or are they a prize/reward to be won? Are their bodies used primarily for audience titillation, with little regard for the person?
A character who engages with sex because they want to is sex-positive. A character who has sex because the writer wants to have sex with them, or wants the players to be jerking off to them, or because some other character wants to have sex with them, is a sexual object.
If the origin characters, narratively, function fine without any romance or sex. And if their romances do not take away from that. Then these characters are not objectified, no matter how horny they may be.
I feel as though you are trying to make a point, and accidentally making the counter case to what you intend. Your post suggests to me that, by your metric, these characters are very much over-sexualised and objectified.
The characters in question do not have agency. They are characters controlled by their writers to respond in particular ways to particular flags, no matter what else outside their flag tree (and those flag trees are being revealed to be extremely narrow) the character does. Their agency, as digital constructs, is zero.
The characters you can bed in BG3 are absolutely treated like prizes to be won and the sex is a 'reward' for doing the things they like. Their bodies are absolutely used, in this sense, purely for audience titillation, with No regard for the theoretical person.
They all have sex scenes written for them and gratuitously choreographed (even if said scenes don't land well), because the writers wanted to put sex in the game; there is no reasonable way to deny that and still retain intellectual integrity. The question was never "What is appropriate for the progression of this character", and always "Where and when can we put the sex, so it works?" (and they weren't too fussy about that second question, most of the time, either). Those scenes exist not to further the characters in any tangible way outside of the scenes themselves (they don't), but to deliver sex to the viewing audience as a 'pay off', using the character as a vehicle. That is absolutely sexual objectification, even before we step back from it and take into account that there are no 'people' here - only a video game that pitches digital dolls (sexual objects) at you for your gratification.
If we think only internally to the game space, and consider the characters as people... it doesn't get much better. The relationships you build with them are one dimensional where one direction is "I hate you and want to kill you" and the other is "Lets bang, okay?" and there is no nuance and no in-between (aside from non-interactive non-existence) and no alternative; sex is very much equated with winning in the game of character relationships.
The short answers for your questions above:
"Is the sex on their terms?" - If it were not on agreed terms, there would be no properly informed consent and we'd be talking about rape. You're not saying anything of value here. If you're trying to imply that them making the first move as opposed to the player, somehow makes them less objectified, then no, as written constructs pitched to a viewing audience, it does not. "Are they an active participant?" - As above. "Do they make choices?" - For the most part, no, they don't. Once you get to the "guess it's sex time now" gate, choice vanishes for the most part. But... You know who gets to make even fewer choices about how they want the sex to be? The player character; in almost every case they have to numbly accept sex as delivered by their prize-giver, or opt out entirely. That isn't a point in favour of 'not overly sexualised content'. "Are their wants and needs, considered important?" - As above, no, they aren't, not really... but the player character's needs and wants are considered Even Less. They have to accept the scene and behaviour that the writers wanted to deliver this sex scene in, and be an acting doll in the writer's porn shoot, as directed, or they can cancel it entirely; their actual personal character wants or desires are not considered in virtually every case (and indeed as has been demonstrated, the character is forced to such a soulless stand-in doll that their physical anatomy and gender is not considered for the scene, behind their physical build). "Or are they a prize/reward to be won? Are their bodies used primarily for audience titillation, with little regard for the person?" Yes, 100% absolutely they completely are, in almost every case.
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To be clear for myself, I'm not saying that having heavily sexualised content or characters is bad; to me, it's not! It's just a matter of how it's handled and how well it blends with the world and space it's in; how well it fits meaningfully into the space and the characters. I like it when the characters I'm interacting with are able to be acknowledged as sexual beings, and for each of my characters, in all spaces I roleplay in - be it forum-based, D&D tabletop, or other video games, I generally know what their tastes and preferences are, even if it never really comes up; for me, that's an important facet of their identity and who they are, and it can impact and influence things, and it matters. I appreciate games that take the same degree of fullness to their character design.
What I've found in BG3, however, doesn't do that. The sex is a prize, and a milestone; it never escapes feeing disconnected from anything outside itself, placed purely to reward the player. Anyone who knows me knows I've put a great deal of work into feedback on how to write and choreograph intimate sequences in ways that work, and that it's an area of interest to me, to see sex and intimacy present in a game to give it a real, breathing-world feel... to be able to explore that with my character, and define what they like or want to the game, and have the game pick that up and respond to it... but my interest is in it being done well, and what we have been given in BG3 is not that.