It's difficult.
When they're still fairly new, both kinds of users don't even know that the respective other kind exists. Chances are that discovery ends up rather painful for one or both sides (character-centric user breaks user-centric user's heart in what they believe is just a role-play; user-centric user shatters character-centric user's immersion by blatantly going OOC due to not even having a character in that sense). But if they're lucky, they just find out that people may see avatars differently from how they see avatars without any nasty side-effects.
"Painful" may pretty well describe a situation similar to what Bob Marley described, only that it'd be a result of misunderstanding in OpenSim. Boy and girl meet at a party of sorts, interesting kind of conversation ensues, and it eventually leads to sexy times.
So far, so good.
Now, the boy is the avatar of a character-centric male user who basically just wanted to make a little interactive porn with the girl, expecting her to be just as character-centric as himself.
The girl, however, is the avatar of a user-centric female user who, over the course of the party and the conversation, got completely and utterly smitten over the boy. Or rather her mental image of the user behind the boy, based on a lot of projection plus a little wishful thinking. For her, the virtual sex wasn't just some smutty online role-play, it was an expression of love. Or the kind of obsession that people sometimes mistake for love.
According to Bob Marley, anything the male user would do now that doesn't lead to a long-distance relationship with that female user would be cowardice. (Strictly speaking, women with male avatars who end up being taken for real-life men are exempt from this quote.)
However, if you as a character-centric user experience such a situation, when you notice that the user behind that other avatar has started obsessing over your avatar and their projection of real-life you, it's too late. You're past a point of no return. You can't easily nope out of this whole thing anymore.
Seriously: If such a situation happens, going all the way first and then ghosting the other avatar/user is the best you can do. It's even better than faking a viewer crash and then not coming back which is actually more cowardish and more blatantly so. Or rather than actually ghosting them, you may also announce your likely absence and then actually stay absent like you've announced.
Tell them you aren't online that much, especially not during times when they're online. If they haven't befriended you, you may come online, but stay on your own turf or hypergrid with caution so you won't meet them. If they have befriended you, keep that particular avatar offline when it's likely that they are online. Especially as a character-centric user, you should have at least one spare avatar, preferably one with a wholly different identity that she would never suspect to be an alt of her target of obsession. Keep away from them for a few weeks until they got over you, found someone else or got so disappointed that they'll leave you alone henceforth.
Also, try to resist accepting their friendship offer. If you accept it, they can see whenever you're on and start stalking you.
Telling them in the heat of the moment (and this can still be before the actual sex) that you aren't interested in anything serious and/or permanent will either hurt them and leave them unsatisfied. Or they'll ignore it just as much as when you try to tell them that your real-life gender is not necessarily what they oh so firmly believe it absolutely has to be. People with a rather attractive opposite-gender alt that they let out of the closet every now and then may have experienced the latter first-hand already.
Giving them what they desire, especially if it's a long-distance relationship between two real-life people just based on two avatars meeting and a lot of imagination and projection on one side, will be uncomfortable for you. This has little to do with cowardice. Even less if you're a woman, and another woman is smitten over your handsome male alt and wants to meet the alleged man behind him in real life.
In all seriousness, this isn't all grey theory. I know what I'm writing about. I've had guys obsess over a female alt of mine (I'm not saying which) at least twice already, being absolutely certain that I'm a woman IRL.
The first one was literally the first time one of my avatars got into such a situation. It was at a nude party, she was naked, and he actually stripped down to talk to her. He ended up inviting her to his place. There he kept nagging and nagging me (via her) to tell him everything about my RL, even after "doing it", which I refused at first. The way he talked (or rather wrote) made it seem to me like he was already envisioning a white wedding with my female alt.
Later, I decided to be so honest and tell him my RL gender. He was sick and disgusted and felt like having been tricked into gay sex by a gay man. I understood that, from his POV, it wasn't his avatar fucking mine, it was HIM cyberfucking ME. Or rather him cyberfucking his imagination of who and what I am.
The other one who comes to my mind asked me about my real life, too. Again, I told him it's none of his business. This time, I stuck with that. I didn't want the above situation to repeat. Unlike the example above, this one actually expressed that he was absolutely certain that I'm a woman IRL, it couldn't be any other way. I tried to tell him that he can't know my RL gender for sure, and I may or may not be a woman, but he said, yes, he could, and I'm definitely a woman. I said that's nothing but wishful thinking which he denied. I told him if he absolutely had to find out about my real life, he could look it up on the "1st life" page of my avatar's profile (which, of course, wasn't blank, albeit not too informative). He said he couldn't be bothered to read profiles and wanted me to tell him everything which I kept refusing.
I did let his avatar fuck mine. I neither wanted to pass up on that nor dump him right before it after first having agreed to it before I knew just how much he'd obsess over whom he took me for. That is, again, his real-life self cyberfucked his projection of real-life me instead.
He had already told me when he's on and when he isn't, and after having sex, he wanted to meet me again in that same place as soon as possible. I had my avatar say she can't promise anything, and she isn't on that often. Unfortunately, I had accepted his friendship offer out of good manners and keeping up the act for as long as I still had to, so he'd know when she's online.
The best I could do then was to keep that particular female alt offline when he'd be online, not to mention away from that place, for a number of weeks. The next time another avatar of mine saw him, he seemed to be chatting up another lady. Success on my side with no substantial damage done to the other side.
The first guy may have been aware that there may be male users behind a female avatar. The second guy told me he was. But both believed they "knew" that this could impossibly be the case with my female alt.
So here's one more advice for the male users: If you want to create a female alt, don't make her a Venus flytrap. Don't make her too attractive. Don't make her stand out too much in a positive way. At least not when she's among other avatars. And don't make her look like she has indeed been created by a female user. That helps avoid such situations.
Also, never tell them where to find you usually. Especially never give them landmarks to your usual hangouts. And don't let them know where exactly you live in-world, neither by landmark nor by OSW link nor by having your home as a pick in your profile with a hop address that leads directly to your home. Otherwise, chances are they'll stalk you. I've experienced that as well.
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