Sure have had my share of weird moments in rp.
My first rp experiences were on a list that sounded very promising, all sorts of characters and personalities from various times and places, though it wasn't limited to fictional characters, people could rp personalities from history too - including famous Bible people. I never really liked that, and places like Quotev have taken this a step further to include fan fiction about real people living today, so they can rp/write out their Directioner/Bieber fantasies for anyone to see. I prefer sticking to rp-ing fictional characters, with the real people being inserted occasionally being limited to the players themselves, for comedy effect, or for slightly deeper reasons like proving that I can kill off a notoriously bad creepy pasta character and nothing bad will happen to me. Because I'm still here.
But that's a slight tangent.
The first weird experience I remember was being quite involved in a plot with a vampire slayer, who had been cool, until it was revealed that he was Lazarus, as in the one raised from death - and since that had happened, he'd encountered a vampire that bit him and made him immortal and he never wanted to live in the first place. So the take-away was basically implying that what Jesus did, sucked. And this was a famous Bible character, not a make-believe "once upon a time" sort.
I don't know how I jammed out of that plot, think I just told the writer I wasn't cool with that, and my character wouldn't be either, so just bowed out. He took it just fine. There were plenty of others willing to do that kind of fiction over there.
On another rp, I learned that both main characters were Mary sues. One had linked her life via some kind of psychic bond to the main canon character, and was a girl friend to another lesser known famous fictional character that had been turned into a human for that purpose. Double Mary Sue.
The other character had a thing for the guy who was young enough to be her son, because he had bullied her adopted son (main canon character) in school. And when I mean she had a thing for him, I mean, she fell in love with him at some point when those boys had grown up. Ugh! The author's justifying of this twisted repulsive idea was that her character was super good at reading people's character, so this had to be the fault she had, to make her and her power not perfect.
Eww.
That definitely wasn't what I thought I was signing up for.
This isn't exactly rp, but closely related.
I wanted to rp with this person, who seemed really classy, on the surface. And she was being horribly harassed by cyber bullies. I was just learning what Mary Sues were. I gave it to her bullies with both barrels. Any in-character stuff I wrote about Lady One to make her laugh, and tick her flamers off to no end, got a really curious reaction from her. She always praised my writing, but added "You don't show even a hint of jealousy about Lady Une." My reaction was always "Why the heck would I be jealous of her?" I knew her bullies were jealous because she replaced Lady Une with her own Mary Sue whenever she wrote about that stupid Treize Khushr-aw, scrap that freakishly long ree-darn-diculous name of his. I always thought she was way too stuck on him, and saw nothing in him. But I had believed the jealousy had come from only the bullies, who were childish enough to fight over a cartoon character they crushed on.
Eventually, I learned that she was jealous of Lady une, and put so much into how characters looked. She couldn't rp with me because I was all about plot and character interaction. She was all about snogging Treize K, and out-shining every other female around. so she couldn't rp with my characters because they couldn't care less about Treize, or how Mary Sue's hair looked, or how she had a luminous dark-eyed stare that was so hot it could melt chocolate 20 steps away. No kidding, she actually wrote that. And when I happened on one of her erotic stories, it made me gag.
Yeah, when characters, writers, and plot schemes turn out to be nothing like you thought they were, it gets off-putting, fast.
Oh BTW, the male version of a Mary Sue is a Gary or Marty Stu.