[RPG] lways a “designated” person to lead/move the party

Misogyny disguised as humour is still misogyny

And, more generally, any form of bigotry disguised as humour is still bigotry. As a white, middle-aged, middle-class male my experience of bigotry is far more likely to be as a perpetrator than as a victim. Because that's not the person I want to be, I take my cues on what is and is not acceptable from the people who are more likely to be victims.

Raise your concerns. Politely.

Bigot and misogynist are insults - with few exceptions, nobody likes to think of themselves by those labels.

A far more productive approach is to recognize that no one can be a bigot in the way that someone can be, say, an American. A 'bigot' is not a thing you are but at certain times we all say bigoted things or carry out bigoted actions. Dealing with it requires an understanding that good people sometimes do bad things and if they want to do bad things less often they have to be able to recognize the bad things without thinking of themselves as bad people.

Something like:

Hey, I want to talk about what's going on between Lady and Man. Last session it got pretty violent and we all had a laugh about some old sexist stereotypes. However, on reflection, I'm not comfortable with where it went and where it seems it might go in the future - it's not the type of situation that I'd want to see my sister/mother/girlfriend in, and while I know it's all make-believe, this is not an area I want to explore through role-play. Can we tone it down?

And then listen.

Don't expect behaviour to change in one go

If they agree to "tone it down" you may find that this doesn't stick. This isn't a snub to you. Behavior change is hard. You will need to be prepared for backsliding and to gently remind them that you all agreed you weren't going to do this anymore.

Be prepared to walk

If this doesn't change and it makes you so uncomfortable that you aren't enjoying yourself - stop.

It's a big wide world out there full of role playing games.

It depends on your table, so ask your table; here are some different ways I've run it at my own

There are a few different ways I've tackled the "RP vs. skill level problem" and I usually just ask the group which they'd prefer unless a campaign demands one method over another:

1. RP determines everything, no skill checks exist

   Note that this doesn't completely remove skill proficiencies from being helpful; they may still have in-combat uses or some sort of other feature might call for a skill check, but this is far from an ideal option. (You may end up having to rearrange class proficiencies as many end up being near-useless)

2. RP determines the result, skill check determines any additional circumstances

   Here I have the character (player) RP and this (depending on how well they do it) determines what the result of the NPC encounter is. I then have them make a check to see whether it goes off with some extra stipulations, perhaps nothing goes wrong, or the NPC throws in an extra incentive. One benefit of this style is that it prevents players from having to RP characters who are less, or even worse more persuasive/whatever than themself. An often difficult thing to do, but one that can be done.

3. Skill check determines the result, RP determines additional circumstances

   This is basically the above but reversed, putting less pressure on the Player's ability to perform the skill as RP and more of fate is left up to the dice and the character's own proficiency in said skill.

4. Skill check determines everything, RP simply follows

   Here the player (though not the character) already knows whether they succeed or fail, which gives them a bit of an idea of what to be arriving for. They can model how well they argue based off of the roll, some tables have preferred this method but it certainly teeters on the edges of meta-gaming and is hard to get a good balance for. It also still promotes having a high skill level as this increases the odds of a good result, and even is the only way to get a great result.

5. Skill level determines possible results

   This is the method I most often use though it is unusual. Here I have thresholds like the following: if your passive persuasion is at least 16, you can get the great result, otherwise you can only get a good result. This method leaves less up the rolls of the dice, and gives a greater benefit to simply having a greater proficiency in some given skill. You'll note that I've left out how to actually determine the result and that's because when using this method I always ask my table how they want this to work. Sometimes there is no skill check at all, sometimes the RP is just for flavor and the passive score dictates everything (though this has the negative side-effect of promoting just having one party member being good at each skill and thus nearly-always succeeding at any sort of skillful endeavor).

Overall you've got a lot of options, including many besides the ones here, for how to handle RP and skill checks. Sometimes, unavoidably, they won't line up or really agree with each other at all, and I suggest discussing what to do in this sort of scenario with your players. If the RP is phenomenal and the dice give you the absolute worst roll perhaps some sort of bonus is in order? One thing you could do is give advantage to a check if the RP is particularly good, I've done this before as a inspiration-esque method of promoting quality RP from my players.

There are many other things to consider as well, such as quality of RP, creativity, and other less quantifiable and more qualitative aspects of the game. The bottom line (for me) is to ask your players what they want to see in the game.