Oh dear Anon, you have just opened a can of worms with this question.
Before I begin this formidable post however, a short answer.
Yes, not only do I like him, he is my favourite One Piece character, and even after timeskip when he’s often hard to handle, I still love him. Having said that, there are plenty of valid reasons not to like him, and you shouldn’t feel pressured to. Everybody’s different, and his attitude towards women and disregard for the other guys lately make it easy to see why you have trouble liking him, and there’s no shame in that. Truthfully, if he hadn’t already been my favourite for so long beforehand, I probably wouldn’t be able to stand him at this point. That’s the wonder of fangirl goggles.
Now for the long answer [you may want to strap yourself in].
Despite myself, and despite the fact that his actions lately have disgusted me, he is still my favourite. Truthfully, if I wasn’t already deeply invested in his character, post timeskip probably would have ruined him for me, but because he’d already been my fave for five years, I have a higher tolerance for his bullshit.
Things that I do like about him are probably the same things that most other Sanji fans talk about- I love his badass attitude, his tactical smarts, his fighting style, his wit, his fashion sense, his sacrificial and caring nature, his relationship with Zeff and the other Baratie staff, his relationship with the crew, his cooking prowess- I’m not going to get too into it for fear of being unable to stop, but you get the idea.
The things that bother me with Sanji are exactly those you pointed out- his two-faced attitude for the guys in his crew, and the swooning over Nami and Robin, both of which have gotten worse over timeskip.
All of the characters have flaws- it’s these flaws can make or break characters for readers, depending on whether you identify with them or not. Unfortunately Sanji’s are more grounded in real world behaviour that a lot of us put up with everyday then, say, Luffy’s ability to eat ten times his weight in food. Combined with his flanderisation over the years [largely because he is the vehicle that Oda has been using for most of his questionable style changes], this makes him a controversial and often out of place character compared to the rest of the crew.
At his introduction, he was a chivalrous young man who was unaware of how his actions made women uncomfortable, and whose treatment of the other male crewmates stemmed from his relationships with the other chefs onboard the Baratie. His behaviours were realistically grounded from his origins, but over the years he’s gotten more and more out of place.
I had always hoped that overcoming his worship of women would be part of his character development, and I can even remember thinking that after the Kalifa fight he might have learnt his lesson [yes you can laugh at me now], then it was after Kamabakka Kingdom, then it was after the blood transfusion, and most recently it was after the bodyswap. Unfortunately, none of these hopes came to fruition, and instead he’s been making a right ass of himself the last two years, with only a couple of fight and strategic scenes to redeem himself.
Sanji’s actions after timeskip feel representative of the larger, more troublesome changes in One Piece. It’s not just that he’s acting like an asshole, molesting Nami, and creeping on the other women, it’s the fact that the audience is supposed to be on his side.
It’s the fact that every female character is identified as a woman first, and a character second, as evidenced by the way that every time a woman is introduced someone has to comment on it: Tashigi’s men calling her Cutie Captain, the mermaids being the beautiful objects of men’s dreams, Shirahoshi being the Mermaid Princess, whose defining feature prior to introduction was that she was supposed to be the most beautiful woman in the world [even more beautiful than Boa Hancock, the previously established most beautiful woman in the world], Kinemon’s introduction to the crew including defining Nami as breast-band girl, and Sanji and the G-5 stopping to swoon over Monet.
There’s also the dehumanisation of crossdressers, where the inhabitants of Kamabakka Kingdom are treated as jokes because they are biological men who identify as women. While Bon Clay, Ivankov and Inazuma are rounded characters, the rest of the crossdressers are written off as a joke, simultaneously reinforcing the beauty standards that OP already applies- they all have the same facial structure as Gatherine, and the stereotype of queer men chasing after unwilling straight guys. Sanji refers to the island as ‘Hell’, and Splash and Splatter are used to further re-iterate Sanji’s opinions about crossdressers, for the assumed amusement of the audience.
While I’m not going to get too into this one, since I already did a post on it here [although I swear if I link to that post one more time I’m just going to suck it up and make a proper repost version that is easier to read] one of the biggest changes is that unlike in earlier chapters where either Usopp, Zoro or Nami would call him out on his bullshit, nobody steps up to Nami’s defence in chapter 663. We’re supposed to side with Sanji and think that it’s awesome that he’s finally gotten a chance to feel up a girl 'because he’s been away from women for two years’, and that Nami is just over-reacting.
With all of these characterisations combined at this point it feels like his faults are wilful ignorance. How he can have come from Kamabakka, where he spent two years being treated by other men the way he treats women, and be even more ignorant to how his actions affect them befuddles me. One Piece often deals in the absurd, but this is just ridiculous.
Even more difficult to take seriously is his latest re-iteration of 'I’d rather die than hurt a woman’, when this takes place only a few hours after he repeatedly groped Nami’s body against her will until she was in tears [chapter 663]. From the original parameters we were given for his character, there’s no way he should have done that. I had always assumed that if a woman told him to stop, he would, bowing to her wishes like he does in every other thing in his life.
Given that Smoker showed a similar attitude to Tashigi’s body [opening off her shirt, taking off her bra, ignoring her requests for him to close her shirt], and Caribou’s gross mermaid abduction scenes, it really feels far more like Oda’s value dissonance than Sanji’s.
So I guess what it comes down to for me is that yes- Sanji has been an ass since timeskip- I cannot, and will not, excuse, ignore, or trivialise his actions, but the issues I’ve had with his character are ones that have been present in One Piece as a whole, not simply as a form of character development for Sanji. Due to this, I am able to look beyond his behaviour, and still find enjoyment in his character, both now in his actions with the G-5 and his fight scenes, and also in the older arcs.
For now that’s enough to get me by.
Of course, as I said before, you don’t need to like Sanji. There is no necessity, no reason, and you should not feel pressured to [I say should, not will not, because unfortunately there are always a few ’true fans’ lurking around], and if you feel that his character flaws overshadow his better traits that’s completely fine.
Either way, I hope my answer has helped.