Since this thread seems fairly reasonable I'll weigh in on this topic just this once, just from my perspective because that's all I have.
"Specific aspects that people, women in particular, find most abrasive?"
It was a long time before I played bayonetta. The "sexy, sexy" protagonist was what put me off for so long, because usually it's only rubbish games that resort to having a oh so sexy female character to draw in the sales.
At the end of the day it was the gameplay that did it and it was brilliant. But the fact is the character didn't get on my nerves either. She was strong, confident, didn't whine, no stupid jiggle physics and her sexuality was flamboyantly silly rather than...seedy (even if some of the unlockable costumes were....).
That's why I'm not getting lollipop chainsaw, the gameplay looks passable but not worth playing as a giggling highschool cheerleader where I get achievements for looking up her skirt. The same probably goes for a game like the new duke nukem, I might've one day got it in a bargain bin as a dumb and fun shooter, but if the developers were so...desperate that they included twins giving oral sex and babe capturing/spanking then no.
However I have to admit it's not a real "moral" stance for me. More just a case of rolling my eyes at how idiotic it is and using it as an indicator that it's probably a rubbish game.
How do these elements effect engagement and involvement?
Not at all for bayonetta, the other two enough for me to avoid completely.
The only real aspect that made me pause for a second in mass effect 2 was when it came to relationships with female crewmembers. IIRC They all boiled down to...
1) Sex
2) complete indifference/dislike
But given every path had to be completely scripted/voice acted it's not exactly a huge issue, just something I noticed. That's pretty much the same as pretty much every hollywood blockbuster anyway.
"What would be some of the aspects that could empower, humanize, engagement?"
Probably not much I can meaningfully say on the empowerment front, since I'm a guy.
In terms of the characters being humanised...bayonetta is an over the top bullet time witch who cooly dispatches planet sized beings...
Tomb raider did it really well with Lara (minor spoiler ahead). Sure, she's pretty, but she was a fleshed out character. As a sidenote I didn't have a problem with the almost rape scene either. Pretty much exactly the same scenario happens in every stranded on island story ever, except here she defends herself and kills the would be rapist. I'm fine with that.
"And lastly, if you wanted some titillation, what could be added, or subtracted, to character, story, design, to add a little 'special' appeal?"
Obviously context, character and character design matters, having a bikini clad girl surrounded by armoured guys is plain stupid and so on...
But an easy aspect to address is...presentation. I can appreciate shots that look like they belong in an action film, not a porn film. When a sexy character appears in an action film you get slow motion, whole body panning etc. It's only in pornos and some comedies that you get close ups of parts jiggling around, upskirts and mass cleavage. Are both sexist? Not my concern, but the latter is tasteless.
However (and this is a point that might catch me a bit of flack) it can "fit" if it's in ridiculous fighting games. The ones where every character is basically a dumb stereotype. The asian blackbelt, indian psychic, fat american, sexy siren, drunk hobo. Sure it's a bit much when every female is oh so sexy, but it's a dumb fighting game, it's all tasteless fun and we all know it. Is it morally right or wrong? I'm not too bothered. Does that mean I support the recent sorceress fiasco? I don't know, but the game looks rubbish anyway.
There are probably areas of this post that are a bit contradictory, but I'm just going to cop out of them by listing context and presentation as the reasons. I didn't come to conclusions from cold hard logic or well thought out arguments. I have no arguments. I have no agenda. We're talking about videogames.
Damn that post was longer than I expected it to be.